Tag Archives: Fluid Dynamics

Fundamental scales in the kinematic phase of the turbulent dynamo [SSA]

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http://arxiv.org/abs/2204.00828


The turbulent dynamo is a powerful mechanism that converts turbulent kinetic energy to magnetic energy. A key question regarding the magnetic field amplification by turbulence, is, on what scale, $\kp$, do magnetic fields become most concentrated? There has been some disagreement about whether $\kp$ is controlled by the viscous scale, $\knu$ (where turbulent kinetic energy dissipates), or the resistive scale, $\keta$ (where magnetic fields dissipate). Here we use direct numerical simulations of magnetohydrodynamic turbulence to measure characteristic scales in the kinematic phase of the turbulent dynamo. We run $104$-simulations with hydrodynamic Reynolds numbers of \mbox{$10 \leq \Reyk \leq 3600$}, and magnetic Reynolds numbers of \mbox{$270 \leq \Reym \leq 4000$}, to explore the dependence of $\kp$ on $\knu$ and $\keta$. Using physically motivated models for the kinetic and magnetic energy spectra, we measure $\knu$, $\keta$ and $\kp$, making sure that the obtained scales are numerically converged. We determine the overall dissipation scale relations \mbox{$\knu = (0.025^{+0.005}{-0.006})\, k\turb\, \Reyk^{3/4}$} and \mbox{$\keta = (0.88^{+0.21}{-0.23})\, \knu\, \Pranm^{1/2}$}, where $k\turb$ is the turbulence driving wavenumber and $\Pranm=\Reym/\Reyk$ is the magnetic Prandtl number. We demonstrate that the principle dependence of $\kp$ is on $\keta$. For plasmas where $\Reyk \gtrsim 100$, we find that \mbox{$\kp = (1.2_{-0.2}^{+0.2})\, \keta$}, with the proportionality constant related to the power-law `Kazantsev’ exponent of the magnetic power spectrum. Throughout this study, we find a dichotomy in the fundamental properties of the dynamo where $\Reyk > 100$, compared to $\Reyk < 100$. We report a minimum critical hydrodynamic Reynolds number, $\Reyk_\crit = 100$ for bonafide turbulent dynamo action.

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N. Kriel, J. Beattie, A. Seta, et. al.
Tue, 5 Apr 22
40/83

Comments: 15 pages, 10 figures

Annular structures in perturbed low mass disc-shaped gaseous nebulae I : general and standard models [EPA]

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http://arxiv.org/abs/2204.01135


This is the first of two papers where we study analytical solutions of a bidimensional low mass gaseous disc rotating around a central mass and submitted to small radial perturbations. Hydrodynamics equations are solved for the equilibrium and perturbed configurations. A wave-like equation for the gas perturbed specific mass is deduced and solved analytically for several cases of exponents of the power law distributions of the unperturbed specific mass and sound speed. It is found that, first, the gas perturbed specific mass displays exponentially spaced maxima, corresponding to zeros of the radial perturbed velocity; second, the distance ratio of successive maxima of the perturbed specific mass is a constant depending on disc characteristics and, following the model, also on the perturbation’s frequency; and, third, inward and outward gas flows are induced from zones of minima toward zones of maxima of perturbed specific mass, leading eventually to the possible formation of gaseous annular structures in the disc. The results presented may be applied in various astrophysical contexts to thin gaseous discs of negligible relative mass, submitted to small radial perturbations.

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V. Pletser
Tue, 5 Apr 22
55/83

Comments: 17 pages, 1 Figure. Submitted to Astrophysics and Space Science

Moosinesq Convection in the Cores of Moosive Stars [SSA]

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http://arxiv.org/abs/2204.00002


Stars with masses $\gtrsim 4 \times 10^{27}M_{\rm{moose}} \approx 1.1 M_\odot$ have core convection zones during their time on the main sequence. In these moosive stars, convection introduces many uncertainties in stellar modeling. In this Letter, we build upon the Boussinesq approximation to present the first-ever simulations of Moosinesq convection, which captures the complex geometric structure of the convection zones of these stars. These flows are bounded in a manner informed by the majestic terrestrial Alces alces (moose) and could have important consequences for the evolution of these stars. We find that Moosinesq convection results in very interesting flow morphologies and rapid heat transfer, and posit this as a mechanism of biomechanical thermoregulation.

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E. Anders, E. Bauer, A. Jermyn, et. al.
Mon, 4 Apr 22
9/50

Comments: 7 pages, 3 figures, 1 moose, no logic in this place

Ion Alfvén velocity fluctuations and implications for the diffusion of streaming cosmic rays [GA]

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http://arxiv.org/abs/2203.13952


The interstellar medium (ISM) of star-forming galaxies is magnetized and turbulent. Cosmic rays (CRs) propagate through it, and those with energies from $\sim\,\rm{GeV} – \rm{TeV}$ are likely subject to the streaming instability, whereby the wave damping processes balances excitation of resonant ionic Alfv\’en waves by the CRs, reaching an equilibrium in which the propagation speed of the CRs is very close to the local ion Alfv\’en velocity. The transport of streaming CRs is therefore sensitive to ionic Alfv\’en velocity fluctuations. In this paper we systematically study these fluctuations using a large ensemble of compressible MHD turbulence simulations. We show that for sub-Alfv\’enic turbulence, as obtains for a strongly magnetized ISM, the ionic Alfv\’en velocity probability density function (PDF) is determined solely by the density fluctuations from shocked gas forming parallel to the magnetic field, and we develop analytical models for the ionic Alfv\’en velocity PDF up to second moments. For super-Alfv\’enic turbulence, magnetic and density fluctuations are correlated in complex ways, and these correlations as well as contributions from the magnetic fluctuations sets the ionic Alfv\’en velocity PDF. We discuss the implications of these findings for underlying “macroscopic” diffusion mechanisms in CRs undergoing the streaming instability, including modeling the macroscopic diffusion coefficient for the parallel transport in a sub-Alfv\’enic plasma. We also describe how, for highly-magnetized turbulent gas, the gas density PDF, and hence column density PDF, can be used to access information about ionic Alfv\’en velocity structure from observations of the magnetized ISM.

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J. Beattie, M. Krumholz, C. Federrath, et. al.
Tue, 29 Mar 22
10/73

Comments: Invited submission to Frontiers in Astronomy and Space Sciences: Multi-scale Magnetic Field Measurements in the Multi-Phase Interstellar Medium; 43 pages; 11 Figures, 2 tables

Provably Positive Central DG Schemes via Geometric Quasilinearization for Ideal MHD Equations [CL]

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http://arxiv.org/abs/2203.14853


In the numerical simulation of ideal MHD, keeping the pressure and density positive is essential for both physical considerations and numerical stability. This is a challenge, due to the underlying relation between such positivity-preserving (PP) property and the magnetic divergence-free (DF) constraint as well as the strong nonlinearity of the MHD equations. This paper presents the first rigorous PP analysis of the central discontinuous Galerkin (CDG) methods and constructs arbitrarily high-order PP CDG schemes for ideal MHD. By the recently developed geometric quasilinearization (GQL) approach, our analysis reveals that the PP property of standard CDG methods is closely related to a discrete DF condition, whose form was unknown and differs from the non-central DG and finite volume cases in [K. Wu, SIAM J. Numer. Anal. 2018]. This result lays the foundation for the design of our PP CDG schemes. In 1D case, the discrete DF condition is naturally satisfied, and we prove the standard CDG method is PP under a condition that can be enforced with a PP limiter. However, in the multidimensional cases, the discrete DF condition is highly nontrivial yet critical, and we prove the the standard CDG method, even with the PP limiter, is not PP in general, as it fails to meet the discrete DF condition. We address this issue by carefully analyzing the structure of the discrete divergence and then constructing new locally DF CDG schemes for Godunov’s modified MHD equations with an additional source. The key point is to find out the suitable discretization of the source term such that it exactly offsets all the terms in the discrete DF condition. Based on the GQL approach, we prove the PP property of the new multidimensional CDG schemes. The robustness and accuracy of PP CDG schemes are validated by several demanding examples, including the high-speed jets and blast problems with very low plasma beta.

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K. Wu, H. Jiang and C. Shu
Tue, 29 Mar 22
50/73

Comments: N/A

AI Poincaré 2.0: Machine Learning Conservation Laws from Differential Equations [CL]

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http://arxiv.org/abs/2203.12610


We present a machine learning algorithm that discovers conservation laws from differential equations, both numerically (parametrized as neural networks) and symbolically, ensuring their functional independence (a non-linear generalization of linear independence). Our independence module can be viewed as a nonlinear generalization of singular value decomposition. Our method can readily handle inductive biases for conservation laws. We validate it with examples including the 3-body problem, the KdV equation and nonlinear Schr\”odinger equation.

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Z. Liu, V. Madhavan and M. Tegmark
Thu, 24 Mar 22
21/56

Comments: 17 pages, 10 figures

Spin precession in the gravity wave analogue black hole spacetime [CL]

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http://arxiv.org/abs/2203.11459


It was predicted that the spin precession frequency of a stationary gyroscope shows various anomalies in the strong gravity regime if its orbit shrinks, and eventually its precession frequency becomes arbitrarily high very close to the horizon of a rotating black hole. Considering the gravity waves of a flowing fluid with vortex in a shallow basin, that acts as a rotating analogue black hole, one can observe the predicted strong gravity effect on the spin precession in the laboratory. Attaching a thread with the buoyant particles and anchored it to the bottom of the fluid container with a short length of miniature chain, one can construct a simple local test gyroscope to measure the spin precession frequency in the vicinity of the gravity wave analogue black hole. The thread acts as the axis of the gyroscope. By regulating the orbital frequency of the test gyroscope, one can also be able to measure the strong gravity Lense-Thirring effect and geodetic/de-Sitter effect with this experimental set-up, as the special cases. For example, to measure the Lense-Thirring effect, the length of the miniature chain can be set to zero, so that the gyroscope becomes static. One can also measure the geodetic precession with this system by orbiting the test gyroscope in the so-called Keplerian frequency around the non-rotating analogue black hole that can be constructed by making the rotation of the fluid/vortex negligible compared to its radial velocity.

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C. Chakraborty and B. Mukhopadhyay
Thu, 24 Mar 22
24/56

Comments: 12 pages including 4 figures; Version published in Universe

The baryonic-to-halo mass relation from mass and energy cascade in self-gravitating collisionless dark matter flow [GA]

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http://arxiv.org/abs/2203.06899


The relation between properties of galaxies and dark matter halos they reside in can be valuable to understand structure formation and evolution, particularly the baryonic-to-halo mass ratio (BHMR) and its dynamic evolution. We first review some unique properties of self-gravitating collisionless dark matter flow (SG-CFD), followed by their implications in derivation of BHMR. To maximize system entropy, the long-range interaction requires a broad size of halos to be formed. These halos facilitate an inverse mass and energy cascade from small to large mass scales that involves a constant rate of energy transfer $\epsilon_u$=$-4.6\times10^{-7}m^2/s^3$. Considering galaxies and halos with a total baryonic mass $m_b$, halo mass $m_h$, halo virial size $r_h$, and flat rotation velocity $v_f$, the baryonic-to-halo mass relation can be analytically derived by combining the baryonic Tully-Fisher relation and constant rate of energy cascade $\epsilon_u$. We found a maximum BHMR ratio ~0.076 for halos with a critical mass $m_{hc}$~$10^{12}M_{sun}$ at z=0. That ratio is much lower for both smaller and larger halos such that two regimes can be identified: i) for incompressible small halos with mass $m_h$<$m_{hc}$, we have $\epsilon_u$$\propto$$v_f/r_h$, $v_f$$\propto$$r_h$, and $m_b$$\propto$$m_h^{4/3}$; ii) for large halos with mass $m_h$>$m_{hc}$, we have $\epsilon_u$$\propto$$v_f^3/r_h$, $v_f$$\propto$$r_h^{1/3}$, and $m_b$$\propto$$m_h^{4/9}$. Combined with proposed double-$\lambda$ halo mass function, the average BHMR ratio for all halos (~0.024 at z=0) can be analytically derived, along with its redshift evolution. The fraction of baryons in galaxy is ~7.6% at z=0 and increases with time $\propto$$t^{1/3}$. Most (~92.4%) of the baryons are not in galaxies. The SPARC (Spitzer Photometry & Accurate Rotation Curves) data with ~175 late-type galaxies were used for the derivation and comparison.

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Z. Xu
Tue, 15 Mar 22
68/108

Comments: 23 pages, 11 figures, 2 tables

Schwarzschild and Ledoux are equivalent on evolutionary timescales [SSA]

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http://arxiv.org/abs/2203.06186


Stellar evolution models calculate convective boundaries using either the Schwarzschild or Ledoux criterion, but confusion remains regarding which criterion to use. Here we present a 3D hydrodynamical simulation of a convection zone and adjacent radiative zone, including both thermal and compositional buoyancy forces. As expected, regions which are unstable according to the Ledoux criterion are convective. Initially, the radiative zone adjacent to the convection zone is Schwarzschild-unstable but Ledoux-stable due to a composition gradient. Over many convective overturn timescales the convection zone grows via entrainment. The convection zone saturates at the size originally predicted by the Schwarzschild criterion, although in this final state the Schwarzschild and Ledoux criteria agree. Therefore, the Schwarzschild criterion should be used to determine the size of stellar convection zones, except possibly during short-lived evolutionary stages in which entrainment persists.

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E. Anders, A. Jermyn, D. Lecoanet, et. al.
Tue, 15 Mar 22
88/108

Comments: Manuscript accepted in ApJ Letters. Supplemental materials are in a Zenodo repository (this https URL). Code is in a Github repository (this https URL)

The origin of MOND acceleration and deep-MOND behavior from mass and energy cascade in dark matter flow [CEA]

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http://arxiv.org/abs/2203.05606


The MOND paradigm is an empirical theory with modified gravity to reproduce many astronomical observations without invoking the dark matter hypothesis. Instead of falsifying the existence of dark matter, we propose that MOND is an effective theory naturally emerging from the long-range and collisionless nature of dark matter flow. It essentially describes the dynamics of baryonic mass suspended in fluctuating dark matter fluid. We first review the unique properties of self-gravitating collisionless dark matter flow (SG-CFD), followed by their implications in the origin of MOND theory. To maximize system entropy, the long-range interaction requires a broad size of halos to be formed. These halos facilitate an inverse mass and energy cascade from small to large mass scales that involves a constant rate of energy transfer $\epsilon_u$=$-4.6\times10^{-7}m^2/s^3$. In addition to the velocity fluctuation with a typical scale $u$, the long-range interaction leads to a fluctuation in acceleration with a typical scale $a_0$ that matches the value of critical MOND acceleration. The velocity and acceleration fluctuations in dark matter flow satisfy the equality $\epsilon_u$=$-a_0u/(3\pi)^2$ such that $a_0$ can be determined. A notable (unexplained) coincidence of cosmological constant $\Lambda\propto (a_0/c)^2$ might point to a dark energy density proportional to acceleration fluctuation, i.e. $\rho_{vac}\propto a_0^2/G$. At z=0 with $u$=354.61km/s, $a_0$=$1.2\times10^{-10}m/s^2$ can be obtained. For given particle velocity $v_p$, maximum entropy distributions developed from mass/energy cascade lead to a particle kinetic energy $\epsilon_k\propto v_p$ at small acceleration $<a_0$ and $\epsilon_k\propto v_p^2$ for large acceleration $>a_0$. Combining this with the constant rate of energy transfer $\epsilon_u$, both regular Newtonian dynamics and deep-MOND behavior can be fully recovered.

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Z. Xu
Mon, 14 Mar 22
19/67

Comments: 20 pages, 8 figures

Effective drag in rotating, poorly conducting plasma turbulence [CL]

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http://arxiv.org/abs/2203.04992


Despite the increasing sophistication of numerical models of hot Jupiter atmospheres, the large time-scale separation required in simulating the wide range in electrical conductivity between the dayside and nightside has made it difficult to run fully consistent magnetohydrodynamic (MHD) models. This has led to many studies that resort to drag parametrizations of MHD. In this study, we revisit the question of the Lorentz force as an effective drag by running a series of direct numerical simulations of a weakly rotating, poorly conducting flow in the presence of a misaligned, strong background magnetic field. We find that the drag parametrization fails once the time-scale associated with the Lorentz force becomes shorter than the dynamical time-scale in the system, beyond which the effective drag coefficient remains roughly constant, despite orders-of-magnitude variation in the Lorentz (magnetic) time-scale. We offer an improvement to the drag parametrization by considering the relevant asymptotic limit of low conductivity and strong background magnetic field, known as the quasi-static MHD approximation of the Lorentz force. This approximation removes the fast time-scale associated with magnetic diffusion, but retains a more complex version of the Lorentz force, which could be utilized in future numerical models of hot Jupiter atmospheric circulation.

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S. Benavides, K. Burns, B. Gallet, et. al.
Fri, 11 Mar 22
19/59

Comments: Main text 9 pages, total 11 pages, 4 figures, 1 table. Submitted to the Astrophysical Journal

Comptonization by Reconnection Plasmoids in Black Hole Coronae II: Electron-Ion Plasma [HEAP]

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http://arxiv.org/abs/2203.02856


We perform two-dimensional particle-in-cell simulations of magnetic reconnection in electron-ion plasmas subject to strong Compton cooling and calculate the X-ray spectra produced by this process. The simulations are performed for trans-relativistic reconnection with magnetization $1\leq \sigma\leq 3$ (defined as the ratio of magnetic tension to plasma rest-mass density), which is expected in the coronae of accretion disks around black holes. We find that magnetic dissipation proceeds with inefficient energy exchange between the heated ions and the Compton-cooled electrons. As a result, most electrons are kept at a low temperature in Compton equilibrium with radiation, and so thermal Comptonization cannot reach photon energies $\sim 100$ keV observed from accreting black holes. Nevertheless, magnetic reconnection efficiently generates $\sim 100$ keV photons because of mildly relativistic bulk motions of the plasmoid chain formed in the reconnection layer. Comptonization by the plasmoid motions dominates the radiative output and controls the peak of the radiation spectrum $E_{\rm pk}$. We find $E_{\rm pk}\sim 40$ keV for $\sigma=1$ and $E_{\rm pk}\sim100$ keV for $\sigma=3$. In addition to the X-ray peak around 100 keV, the simulations show a non-thermal MeV tail emitted by a non-thermal electron population generated near X-points of the reconnection layer. The results are consistent with the typical hard state of accreting black holes. In particular, we find that the spectrum of Cygnus~X-1 is well explained by electron-ion reconnection with $\sigma\sim 3$.

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N. Sridhar, L. Sironi and A. Beloborodov
Tue, 8 Mar 22
27/100

Comments: Submitted for publication in MNRAS: 15 pages, 13 figures, 1 table, 7 appendices. Part-I can be accessed at arXiv:2107.00263

Multi-cavity gravito-acoustic modes in stars: A general analytical resonance condition [SSA]

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http://arxiv.org/abs/2203.03402


Asteroseismology has proven to be a powerful method for probing stellar interiors. Analytical descriptions of the global oscillation modes, in combination with pulsation codes, have provided valuable help in processing and interpreting the large amount of seismic data collected by the CoRoT, $Kepler$, and TESS missions. These prior results have paved the way to more in-depth analyses of the oscillation spectra of stars, which requires innovative theoretical descriptions of stellar oscillations. In this paper, we aim to analytically express the resonance condition of the spheroidal adiabatic oscillation modes in a very general way, applicable at different evolutionary stages. In the present formulation, a star is represented as an acoustic interferometer composed of a multitude of resonant cavities where waves can propagate and the short-wavelength JWKB approximation is met. Each cavity is separated from the adjacent ones by barriers, which corresponds to regions either where waves are evanescent or where the JWKB approximation fails. The stationary modes are computed using two different physical representations: 1) the infinite-time reflections picture 2) the linear boundary value problem picture. Both provide the same resonance condition, which ultimately turns out to depend on a number of parameters: the reflection and transmission phase lags introduced by each barrier, the coupling factor associated with each barrier, and the wave number integral over each resonant cavity. Using such a formulation, we can retrieve the usual forms derived in previous works (e.g., mixed modes with two or three cavities, low- and large-amplitude glitches). This resonance condition provides a new tool that is useful in predicting the stellar oscillation spectra and interpret seismic observations at different evolutionary stages. Practical applications are left to future work.

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C. Pinçon and M. Takata
Tue, 8 Mar 22
31/100

Comments: Accepted for publication in A&A, 20 pages

Cosmic-void observations reconciled with primordial magnetogenesis [CEA]

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http://arxiv.org/abs/2203.03573


It has been suggested that the weak magnetic field hosted by the intergalactic medium (IGM) in voids could be a relic from the early Universe. However, accepted models of turbulent magnetohydrodynamic (MHD) decay predict that the present-day strength of fields generated at the electroweak phase transition (EWPT) should be too low to explain the observed scattering of $\gamma$-rays from TeV blazars. Here, we apply recent theoretical developments — namely, the discovery of the Saffman helicity invariant and of the role of magnetic reconnection in setting the decay rate — to show that the accepted models greatly underpredict the present-day strength of relic fields. Our estimates restore the consistency of the EWPT-relic hypothesis with observational constraints; moreover, we find that efficient magnetogenesis at the EWPT could produce relics with the strength that is believed sufficient to resolve the Hubble tension and explain galaxy-cluster magnetic fields without invoking dynamo amplification.

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D. Hosking and A. Schekochihin
Tue, 8 Mar 22
67/100

Comments: 19 pages, including supplementary information; 6 figures

A dynamo simulation generating Saturn-like small magnetic dipole tilts [EPA]

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http://arxiv.org/abs/2203.03520


Among planetary dynamos, the magnetic field of Saturn stands out in its exceptional level of axisymmetry. One of its peculiar features is that the magnetic dipole mode is tilted with respect to the planetary rotation axis by only $\approx 0.007^{\circ}$ or less. Numerical dynamo simulations performed in this context have had great difficulty in producing such small dipole tilt angles without introducing ad hoc ingredients such as a latitudinally varying heat flux pattern in the outer layers or stably stratified layers (SSL). Here we present a numerical dynamo simulation that generates a highly axisymmetric dynamo with a dipole tilt of about $\approx 0.0008^{\circ}$ on average. The model consists of a deep dynamo layer and an overlying low-conductivity layer but without any SSL. We highlight a novel mechanism where strong differential rotation generated in the atmospheric layer penetrates into the dynamo region, helping to maintain a very small magnetic dipole tilt.

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R. Yadav, H. Cao and J. Bloxham
Tue, 8 Mar 22
86/100

Comments: To appear in Geophysical Research Letters; 11 pages, double columns

3D Radiative Hydrodynamic Modeling of the Near-Surface Shear Layer in the Solar Convection Zone [SSA]

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http://arxiv.org/abs/2203.01484


Understanding effects driven by rotation in the solar convection zone is essential for many problems related to solar activity, such as the formation of differential rotation, meridional circulation, and others. We present realistic 3D radiative hydrodynamics simulations of solar subsurface dynamics in the presence of rotation in a local domain 80 Mm-wide and 25 Mm deep, located at 30 degrees latitude. The simulation results reveal the development of a shallow 10-Mm deep near-surface shear layer (“leptocline”), characterized by a strong radial rotational gradient and self-organized meridional flows. This shear layer is located in the hydrogen ionization zone associated with enhanced anisotropic convective flows overshooting into a relatively stable zone between the H and HeII ionization zones. The radial variations of the differential rotation and meridional circulation profiles obtained from the simulations agree with helioseismic observations, indicating that a major role in forming the leptocline and subsurface meridional flows is played by the local Reynolds stresses.

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I. Kitiashvili, A. Kosovichev, A. Wray, et. al.
Fri, 4 Mar 22
42/63

Comments: 16 pages, 5 figures, submitted to ApJL

Annular structures in perturbed low mass disc-shaped gaseous nebulae II : general and polytropic models [EPA]

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http://arxiv.org/abs/2202.12894


This is the second of two papers where we study additional analytical solutions of a bidimensional low mass gaseous disc rotating around a central mass and submitted to small radial perturbations. In a first Paper, hydrodynamics equations were solved for the equilibrium and perturbed configurations and a wave-like equation for the gas perturbed specific mass was deduced and solved analytically for several cases of exponents of the power law distributions of the unperturbed specific mass and sound speed. In this paper, two other general cases of exponents, including a polytropic case, are solved analytically for small frequencies of the perturbations. Similar conclusions to the ones of Paper I are found, namely that the maxima of the gas perturbed specific mass are exponentially spaced and that their distance ratio is a constant, function of disc characteristics and of the perturbations frequency. Gaseous annular structures would eventually be formed in the disc by inward and outward gas flows from zones of minima toward zones of maxima of perturbed specific mass.

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V. Pletser
Tue, 1 Mar 22
55/80

Comments: 15 pages, 1 Table. Submitted to Astrophysics and Space Science

Energy balance and Alfvén Mach numbers in compressible magnetohydrodynamic turbulence with a large-scale magnetic field [GA]

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http://arxiv.org/abs/2202.13020


Energy equipartition is a powerful theoretical tool for understanding astrophysical plasmas. It is invoked, for example, to measure magnetic fields in the interstellar medium (ISM), as evidence for small-scale turbulent dynamo action, and, in general, to estimate the energy budget of star-forming molecular clouds. In this study we motivate and explore the role of the volume-averaged root-mean-squared (rms) magnetic coupling term between the turbulent, $\delta\mathbf{B}$ and large-scale, $\mathbf{B}0$ fields, $\left< (\delta\mathbf{B}\cdot\mathbf{B}_0)^{2} \right>^{1/2}{\mathcal{V}}$. By considering the second moments of the energy balance equations we show that the rms coupling term is in energy equipartition with the volume-averaged turbulent kinetic energy for turbulence with a sub-Alfv\’enic large-scale field. Under the assumption of exact energy equipartition between these terms, we derive relations for the magnetic and coupling term fluctuations, which provide excellent, parameter-free agreement with time-averaged data from 280 numerical simulations of compressible MHD turbulence. Furthermore, we explore the relation between the turbulent, mean-field and total Alfv\’en Mach numbers, and demonstrate that sub-Alfv\’enic turbulence can only be developed through a strong, large-scale magnetic field, which supports an extremely super-Alfv\’enic turbulent magnetic field. This means that the magnetic field fluctuations are significantly subdominant to the velocity fluctuations in the sub-Alfv\’enic large-scale field regime. Throughout our study, we broadly discuss the implications for observations of magnetic fields and understanding the dynamics in the magnetised ISM.

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J. Beattie, M. Krumholz, R. Skalidis, et. al.
Tue, 1 Mar 22
64/80

Comments: Submitted to MNRAS. 19 pages. 15 figures

Detecting deep axisymmetric toroidal magnetic fields in stars. The traditional approximation of rotation for differentially rotating deep spherical shells with a general azimutal magnetic field [SSA]

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http://arxiv.org/abs/2202.10026


Asteroseismology has revealed small core-to-the-surface rotation contrasts in stars in the whole HR diagram. This is the signature of strong transport of angular momentum (AM) in stellar interiors. One of the plausible candidates to efficiently carry AM is magnetic fields with various topologies that could be present in stellar radiative zones. Among them, strong axisymmetric azimuthal magnetic fields have received a lot of interest. Indeed, if they are subject to the so-called Tayler instability, the accompanying triggered Maxwell stresses can transport AM efficiently. In addition, the electromotive force induced by the fluctuations of magnetic and velocity fields could potentially sustain a dynamo action that leads to the regeneration of the initial strong axisymmetric azimuthal magnetic field. The key question we aim to answer is: can we detect signatures of these deep strong azimuthal magnetic fields? The only way to answer this question is asteroseismology and the best laboratories of study are intermediate-mass and massive stars. Most of these are rapid rotators during their main-sequence. Therefore, we have to study stellar pulsations propagating in stably stratified, rotating, and potentially strongly magnetised radiative zones. We generalise the traditional approximation of rotation by taking simultaneously general axisymmetric differential rotation and azimuthal magnetic fields into account in a non-perturbative way. Using this new formalism, we derive the asymptotic properties of magneto-gravito-inertial (MGI) waves and their period spacings. We find that toroidal magnetic fields induce a shift in the period spacings of MGI modes. An equatorial azimuthal magnetic field with an amplitude of the order of $10^5\,\rm G$ leads to signatures that can be detectable thanks to modern space photometry. More complex hemispheric configurations are more difficult to observe.

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H. Dhouib, S. Mathis, L. Bugnet, et. al.
Tue, 22 Feb 22
42/77

Comments: 21 pages, 15 figures, 3 tables, abstract shortened for arXiv. Accepted for publication in A&A

Turbulent dynamo in the two-phase interstellar medium [GA]

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http://arxiv.org/abs/2202.08324


Magnetic fields are a dynamically important component of the turbulent interstellar medium (ISM) of star-forming galaxies. These magnetic fields are due to a dynamo action, which is a process of converting turbulent kinetic energy to magnetic energy. A dynamo that acts at scales less than the turbulent driving scale is known as the turbulent dynamo. The ISM is a multiphase medium and observations suggests that the properties of magnetic fields differ with the phase. Here, we aim to study how the properties of the turbulent dynamo depend on the phase. We simulate the non-isothermal turbulent dynamo in a two-phase medium (most previous work assumes an isothermal gas). We find that the growth rate of magnetic fields in the exponentially growing stage is similar in both the phases, and this is because of a roughly equal amount of vorticity being generated in each phase. We further compute each term responsible for amplification and destruction of vorticity and show that the amplification of vorticity by turbulent motions is a dominant term (similar in both the phases) followed by the baroclinic term (only present in non-isothermal gases, higher in the warm phase) and the term for viscous interactions in the presence of logarithmic density gradients (higher in the cold phase). We find that the final ratio of magnetic to turbulent kinetic energy is lower due to a stronger Lorentz force. We find that the non-isothermal turbulent dynamo is less efficient than its isothermal counterpart.

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A. Seta and C. Federrath
Fri, 18 Feb 22
6/63

Comments: 16 pages (including 2 appendices), 14 figures (11 in the main text and 3 in the appendices), submitted to MNRAS, comments welcome

Superrotation of Titan's stratosphere driven by the radiative heating of the haze layer [EPA]

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http://arxiv.org/abs/2202.08397


Titan’s stratosphere has been observed in a superrotation state, where the atmosphere rotates many times faster than the surface does. Another characteristics of Titan’s atmosphere is the presence of thick haze layer. In this paper, we performed numerical experiments using a General Circulation Model (GCM), to explore the effects of the haze layer on the stratospheric superrotation. We employed a semi-gray radiation model of Titan’s atmosphere following McKay et al. (1999), which takes account of the sunlight absorption by haze particles. The phase change of methane or the seasonal changes were not taken into account. Our model with the radiation parameters tuned for Titan yielded the global eastward wind around the equator with larger velocities at higher altitudes except at around 70 km after $10^5$ Earth days. Although the atmosphere is not in an equilibrium state, the zonal wind profiles is approximately consistent with the observed one. Analysis on our experiments suggests that the quasi-stationary stratospheric superrotation is maintained by the balance between the meridional circulation decoupled from the surface, and the eddies that transport angular momentum equatorward. This is different from, but similar to, the so-called Gierasch mechanism, in which momentum is supplied from the surface. This structure may explain the no-wind region at about $80$ km in altitude.

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M. Sumi, S. Takehiro, W. Ohfuchi, et. al.
Fri, 18 Feb 22
44/63

Comments: 24 pages, 14 figures, accepted to the Astrophysical Journal

Notes about collapse in magnetohydrodynamics [SSA]

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http://arxiv.org/abs/2202.08121


We discuss a problem about magnetic collapse as a possible process for singularity formation of the magnetic field in a finite time within ideal magneto-hydrodynamics for incompressible fluids. This process is very important from the point of view of various astrophysical applications, in particular, as a mechanism of magnetic filaments formation in the convective zone of the Sun. The collapse possibility is connected with compressibility of continuously distributed magnetic field lines. A well-known example of the formation of magnetic filaments in the kinematic dynamo approximation with a given velocity field, first considered by Parker in 1963, rather indicates that the increase in the magnetic field is exponential in time. In the case of the kinematic approximation for the induction equation, the magnetic filaments formation is shown to occur in areas with a hyperbolic velocity profile.

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E. E.A.Kuznetsov and E. E.A.Mikhailov
Thu, 17 Feb 22
7/60

Comments: N/A

Relativistic Wind Farm Effect: Possibly Turbulent Flow of a Charged, Massless Relativistic Fluid in Graphene [CL]

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http://arxiv.org/abs/2202.07839


At low Reynolds numbers, the wind flow in the wake of a single wind turbine is generally not turbulent. However, turbines in wind farms affect each other’s wakes so that a turbulent flow can arise. In the present work, an analogue of this effect for the massless charge carrier flow around obstacles in graphene is outlined. We use a relativistic hydrodynamic simulation to analyze the flow in a sample containing impurities. Depending on the density of impurities in the sample, we indeed find evidence for potentially turbulent flow and discuss experimental consequences.

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M. Watson
Thu, 17 Feb 22
40/60

Comments: 7 pages, 9 figures

Stability and causality of Carter's multifluid theory [CL]

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http://arxiv.org/abs/2202.06760


Stability and causality are studied for linear perturbations about equilibrium in Carter’s multifluid theory. Our stability analysis is grounded on the requirement that the entropy of the multifluid, plus that of the environment, must be maximised at equilibrium. This allows us to compute a quadratic Lyapunov functional, whose positive definiteness implies stability. Furthermore, we verify explicitly that, also for multifluids, thermodynamic stability implies linear causality. As a notable stability condition, we find that the entrainment matrix must always be positive definite, confirming a widespread intuition.

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L. Gavassino
Tue, 15 Feb 22
33/75

Comments: 16 pages, no figures

Cosmic rays density fluctuations with turbulence universal spectrum -8/3 [HEAP]

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http://arxiv.org/abs/2202.04642


An exact turbulence universal scaling law-8/3 for the density fluctuations of cosmic ray (CR) is obtained on the basis of a new analytical compressible turbulence theory and known two-fluid model of the CR dynamics. It is shown that the origin of this scaling law may be due to the breaking of the nonlinear simple waves in CR medium near the scale of their Larmor radii as for the space plasma of solar wind and magnetosheath.

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A. Chefranov, S. Chefranov and G. Golitsyn
Fri, 11 Feb 22
60/71

Comments: 1 figure

Correlations between turbulent velocity and density fields in the local interstellar medium [GA]

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http://arxiv.org/abs/2202.01610


Turbulence is expected to generate characteristic velocity and density fluctuations in the interstellar medium (ISM). Using HI survey data, we distinguish these contributions as the basis of comparisons with theoretical and magnetohydrodynamical (MHD) simulations. We used HI4PI multiphase observations and Gaussian components representing three HI phases, the cold, warm, and unstable lukewarm medium (CNM, WNM and LNM, respectively) to deduce characteristic fluctuations in turbulent density and velocity fields. We applied the velocity decomposition algorithm (VDA) for separating such fluctuations in the position-position-velocity (PPV) space. The VDA extends the velocity channel analysis (VCA) by Lazarian and Pogosyan and predicts that turbulent velocity and density fields are statistically uncorrelated. Applying the VDA decomposition to the observational data (here, HI4PI) yields – contrary to our expectations – a significant correlation between velocity and density fields. All HI phases contribute to this correlation. The correlations in the velocity wings suffer from attenuation caused by uncorrelated noise. Both VCA and VDA predict that dispersions from fluctuations in narrow velocity channels scale in proportion to the average intensity. Observed brightness temperature fluctuations follow, however, a square-root scaling – as expected for a sum of normally distributed random sources. Fluctuations in HI channel maps at high spatial frequencies are observed to be dominated by density structures, which is in opposition to the results from MHD simulations, where small-scale structures are predicted to have been generated by velocity caustics. The VCA predictions and VDA results on MHD simulations are not compatible with the HI observations. The observed turbulent velocity and density fields in the ISM are not statistically uncorrelated, but they do reveal significant interrelations.

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P. Kalberla, J. Kerp and U. Haud
Fri, 4 Feb 22
46/65

Comments: 15 pages, 15 figures

The statistical theory of self-gravitating collisionless dark matter flow and the correlation, structure, and dispersion functions for velocity, density, and potential fields [CEA]

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http://arxiv.org/abs/2202.00910


N-body simulation is an invaluable tool to understand cosmic velocity field. However, simulation samples velocity only at particle locations that leads to information loss when projecting velocity fields onto structured grid. Here we extract two-point statistics without field projection. These statistics, i.e. correlation/structure/dispersion functions in real space and spectrum functions in Fourier space, are modeled on both small and large scales. Kinematic relations between statistical measures are fully developed for incompressible, constant divergence, and irrotational flow. The nature of flow can be identified by these relations. Much more complex than incompressible flow, peculiar velocity of dark matter flow is of constant divergence on small scale and irrotational on large scale. Incompressible and constant divergence flow share same kinematic relations for even order correlations. The limiting correlation of velocity $\rho_L=1/2$ on the smallest scale ($r=0$) is a unique feature of collisionless flow ($\rho_L=1$ for incompressible flow). Assuming gravity is the only interaction and no radiation produced, this feature leads to an increase in particle mass converted from kinetic energy upon “annihilation”. On large scale, transverse velocity correlation has an exponential form with a comoving scale $r_2$=21.3Mpc/h that maybe related to the size of sound horizon. All other correlation/structure/dispersion/spectrum functions for velocity/density/potential are derived analytically from kinematic relations for irrotational flow. On small scale, longitudinal structure function follows one-fourth law of $S^l_2\propto r^{1/4}$. All other statistical measures are obtained from kinematic relations for constant divergence flow. Vorticity is negatively correlated for $r$ between 1 and 7Mpc/h. Divergence is negatively correlated for $r$>30Mpc/h that leads to negative density correlation.

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Z. Xu
Thu, 3 Feb 22
36/56

Comments: 24 figures, 2 tables

Emergence of long-range correlations and thermal spectra in forced turbulence [CL]

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http://arxiv.org/abs/2202.00462


Recent numerical studies have shown that forced, statistically isotropic turbulence develops a `thermal equilibrium’ spectrum, $\mathcal{E}(k) \propto k^2$, at large scales. This behaviour presents a puzzle, as it appears to imply the growth of a non-zero Saffman integral, which would require the longitudinal velocity correlation function, $\chi(r)$, to satisfy $\chi(r\to \infty)\propto r^{-3}$. As is well known, the Saffman integral is an invariant of decaying turbulence, precisely because non-local interactions (i.e., interactions via exchange of pressure waves) are too weak to generate such correlations. Subject to certain restrictions on the nature of the forcing, we argue that the same should be true for forced turbulence. We show that long-range correlations and a $k^2$ spectrum arise as a result of the turbulent diffusion of linear momentum, and extend only up to a maximum scale that grows slowly with time. This picture has a number of interesting consequences. First, if the forcing generates eddies with significant linear momentum (as in so-called Saffman turbulence), a thermal spectrum is not reached – instead, a shallower spectrum develops. Secondly, the energy of turbulence that is forced for a while and then allowed to decay generically obeys Saffman’s decay laws in the late-time limit.

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D. Hosking and A. Schekochihin
Wed, 2 Feb 22
46/60

Comments: 47 pages, 7 figures, submitted to J. Fluid Mech

The mean flow, velocity dispersion, and evolution of rotating and growing dark matter halos and their effects on the energy transfer in self-gravitating collisionless flow [GA]

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http://arxiv.org/abs/2201.12665


By decomposing velocity dispersions into nonspin- and spin-induced, mean flow and dispersions are analytically solved for axisymmetric rotating and growing halos. The polar flow can be neglected and azimuthal flow is directly related to dispersions. The fictitious (“Reynolds”) stress acts on radial flow to enable energy transfer from mean flow to random motion and maximize system entropy. For large halos (high peak height $\nu$ at early stage of halo life) with constant concentration, there exists a self-similar radial flow (outward in core and inward in outer region). Halo mass, size and specific angular momentum increase linearly with time via fast mass accretion. Halo core spins faster than outer region. Large halos rotate with an angular velocity proportional to Hubble parameter and spin-induced dispersion is dominant. All specific energies (radial/rotational/kinetic/potential) are time-invariant. Both halo spin (~0.031) and anisotropic parameters can be analytically derived. For “small” halos with stable core and slow mass accretion (low peak height $\nu$ at late stage of halo life), radial flow vanishes. Small halos rotate with constant angular velocity and non-spin dispersion is dominant. Small halos are more spherical in shape, incompressible, and isotropic. Radial and azimuthal dispersions are comparable and greater than polar dispersion. Due to finite spin, kinetic energy is not equipartitioned with the greatest energy along azimuthal direction. Halos are hotter with faster spin. Halo relaxation (evolution) from early to late stage involves continuous variation of shape, density, mean flow, momentum, and energy. During relaxation, halo isotopically “stretches” with conserved specific angular kinetic energy, increasing halo concentration and momentum of inertial. Therefore, halo “stretching” leads to decreasing angular velocity and increasing angular momentum and spin parameter.

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Z. Xu
Tue, 1 Feb 22
19/73

Comments: 14 Figure and 4 Tables

Powering Stellar Magnetism: Energy Transfers in Cyclic Dynamos of Sun-like Stars [SSA]

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http://arxiv.org/abs/2201.13218


We use the ASH code to model the convective dynamo of solar-type stars. Based on a series of 15 3-D MHD simulations spanning 4 bins in rotation and mass, we show what mechanisms are at work in these stellar dynamos with and without magnetic cycles and how global stellar parameters affect the outcome. We also derive scaling laws for the differential rotation and magnetic field based on these simulations. We find a weaker trend between differential rotation and stellar rotation rate, ($\Delta \Omega \sim (|\Omega|/\Omega_{\odot})^{0.46}$) in the MHD solutions than in their HD counterpart $(|\Omega|/\Omega_{\odot})^{0.66})$, yielding a better agreement with the observational trends based on power laws. We find that for a fluid Rossby number between $0.15 \lesssim Ro_f \lesssim 0.65$ the solutions possess long magnetic cycle, if $Ro_f \lesssim 0.42$ a short cycle and if $Ro_f \gtrsim 1$ (anti-solar-like differential rotation) a statistically steady state. We show that short-cycle dynamos follow the classical Parker-Yoshimura rule whereas the long-cycle period ones do not. We further demonstrate that the Rossby number dependency of the large-scale surface magnetic field in the simulation ($B_{L,surf} \sim Ro_{f}^{-1.26}$) agrees better with observations ($B_{V} \sim Ro_{s}^{-1.4 \pm 0.1}$) and differs from dynamo scaling based on the global magnetic energy ($B_{bulk} \sim Ro_{f}^{-0.5}$). We also show that up to few percents of the stellar luminosity can be channelled into the star’s magnetism, hence providing a large energy reservoir for possible surface eruptive events.

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A. Brun, A. Strugarek, Q. Noraz, et. al.
Tue, 1 Feb 22
40/73

Comments: 45 pages, 24 figures, 7 tables, 3 appendices, accepted by ApJ on 12/23/21, published on 02/03/22. (1) DAp/AIM, CEA/IRFU, CNRS/INSU, Univ. Paris-Saclay \& Univ. de Paris, France, (2) CMPA, KU Leuven, Belgium, (3) Universidad Carlos III de Madrid, Spain, (4) Dept. de physique, Univ. de Montr\’eal, Canada, (5) JILA and Dept. of Astrophysical and Planetary Sciences, University of Colorado, USA

A hybrid adaptive multiresolution approach for the efficient simulation of reactive flows [CL]

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http://arxiv.org/abs/2201.10686


Computational studies that use block-structured adaptive mesh refinement (AMR) approaches suffer from unnecessarily high mesh resolution in regions adjacent to important solution features. This deficiency limits the performance of AMR codes. In this work a novel hybrid adaptive multiresolution (HAMR) approach to AMR-based calculations is introduced to address this issue. The multiresolution (MR) smoothness indicators are used to identify regions of smoothness on the mesh where the computational cost of individual physics solvers may be decreased by replacing direct calculations with interpolation. We suggest an approach to balance the errors due to the adaptive discretization and the interpolation of physics quantities such that the overall accuracy of the HAMR solution is consistent with that of the MR-driven AMR solution. The performance of the HAMR scheme is evaluated for a range of test problems, from pure hydrodynamics to turbulent combustion.

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B. Gusto and T. Plewa
Thu, 27 Jan 22
34/44

Comments: 24 pages, 13 figures, 3 tables; accepted for publication in Computer Physics Communications; source code available at this https URL

On the Existence of Fast Modes in Compressible Magnetohydrodynamic Turbulence [CL]

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http://arxiv.org/abs/2201.07965


We study the existence and property of Fast magnetosonic modes in 3D compressible MHD turbulence by carrying out a number of simulations with compressible and incompressible driving conditions. We use two approaches to determine the presence of Fast modes: mode decomposition based on spatial variations only and spatio-temporal 4D-FFT analysis of all fluctuations. The latter method enables us to quantify fluctuations that satisfy the dispersion relation of Fast modes with finite frequency. Overall, we find that the fraction of Fast modes identified via spatio-temporal 4D FFT approach in total fluctuation power is either tiny with nearly incompressible driving or ~2% with highly compressible driving. We discuss the implications of our results for understanding the compressible fluctuations in space and astrophysics plasmas.

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Z. Gan, H. Li, X. Fu, et. al.
Fri, 21 Jan 22
28/60

Comments: 8 pages, 5 figures; accepted by the Astrophysical Journal for publication

Focusing of nonlinear eccentric waves in astrophysical discs. II. Excitation and damping of tightly-wound waves [SSA]

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http://arxiv.org/abs/2201.01156


In this paper I develop a nonlinear theory of tightly-wound (highly twisted) eccentric waves in astrophysical discs, based on the averaged Lagrangian method of Whitham. Viscous dissipation is included in the theory by use of a pseudo-Lagrangian. This work is an extension of the theory developed by Lee \& Goodman to 3D discs, with the addition of viscosity. I confirm that linear tightly-wound eccentric waves are overstable and are excited by the presence of a shear viscosity and show this persists for weakly nonlinear waves. I find the waves are damped by shear viscosity when the wave become sufficiently nonlinear, a result previously found in particulate discs. Additionally I compare the results of this model to recent simulations of eccentric waves propagating in the inner regions of black hole discs and show that an ingoing eccentric wave can be strongly damped near the marginally stable orbit, resulting in a nearly circular disc with a strong azimuthal variation in the disc density.

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E. Lynch
Wed, 5 Jan 22
51/54

Comments: 21 pages, 7 figures, Accepted 2021 November 19. Received 2021 November 19; in original form 2021 October 20

Estimations and scaling laws for stellar magnetic fields [SSA]

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http://arxiv.org/abs/2112.15103


For rapidly rotating turbulence (Rossby number much less than unity), the standard mixing length theory for turbulent convection breaks but Coriolis force enters the force balance such that magnetic field eventually depends on rotation. By simplifying the self-sustained magnetohydrodynamics dynamo equations of electrically conducting fluid motion, with the aid of theory of isotropic non-rotating or anisotropic rotating turbulence driven by thermal convection, we make estimations and derive scaling laws for stellar magnetic fields for slow and fast rotation. Our scaling laws are in good agreement with the observations.

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X. Wei
Mon, 3 Jan 22
29/49

Comments: N/A

The Understanding of Intertwined Physics: Discovering Capillary Pressure and Permeability Co-Determination [CL]

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http://arxiv.org/abs/2112.12784


Although capillary and permeability are the two most important physical properties controlling fluid distribution and flow in nature, the interconnectivity function between them was a pressing challenge. Because knowing permeability leads to determining capillary pressure. Geodynamics (e.g., subsurface water, CO2 sequestration) and organs (e.g., plants, blood vessels) depend on capillary pressure and permeability. The first determines how far the fluid can reach, while the second determines how fast the fluid can flow in porous media. They are also vital to designing synthetic materials and micro-objects like membranes and micro-robotics. Here, we reveal the capillary and permeability intertwined behavior function. And demonstrate the unique physical connectors: pore throat size and network, linking capillary pressure and permeability. Our discovery quantifies the inverse relationship between capillary pressure and permeability for the first time, which we analytically derived and experimentally proved.

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O. Alfarisi, D. Ouzzane, M. Sassi, et. al.
Fri, 24 Dec 21
6/58

Comments: N/A

The Understanding of Intertwined Physics: Discovering Capillary Pressure and Permeability Co-Determination [CL]

Posted on by

http://arxiv.org/abs/2112.12784


Although capillary and permeability are the two most important physical properties controlling fluid distribution and flow in nature, the interconnectivity function between them was a pressing challenge. Because knowing permeability leads to determining capillary pressure. Geodynamics (e.g., subsurface water, CO2 sequestration) and organs (e.g., plants, blood vessels) depend on capillary pressure and permeability. The first determines how far the fluid can reach, while the second determines how fast the fluid can flow in porous media. They are also vital to designing synthetic materials and micro-objects like membranes and micro-robotics. Here, we reveal the capillary and permeability intertwined behavior function. And demonstrate the unique physical connectors: pore throat size and network, linking capillary pressure and permeability. Our discovery quantifies the inverse relationship between capillary pressure and permeability for the first time, which we analytically derived and experimentally proved.

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O. Alfarisi, D. Ouzzane, M. Sassi, et. al.
Fri, 24 Dec 21
14/58

Comments: N/A

Stable and unstable supersonic stagnation of an axisymmetric rotating magnetized plasma [CL]

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http://arxiv.org/abs/2112.10828


The Naval Research Laboratory “Mag Noh problem”, described in this paper, is a self-similar magnetized implosion flow, which contains a fast MHD outward propagating shock of constant velocity. We generalize the classic Noh (1983) problem to include azimuthal and axial magnetic fields as well as rotation. Our family of ideal MHD solutions is five-parametric, each solution having its own self-similarity index, gas gamma, magnetization, the ratio of axial to the azimuthal field, and rotation. While the classic Noh problem must have a supersonic implosion velocity to create a shock, our solutions have an interesting three-parametric special case with zero initial velocity in which magnetic tension, instead of implosion flow, creates the shock at $t=0+$. Our self-similar solutions are indeed realized when we solve the initial value MHD problem with finite volume MHD code Athena. We numerically investigated the stability of these solutions and found both stable and unstable regions in parameter space. Stable solutions can be used to test the accuracy of numerical codes. Unstable solutions have also been widely used to test how codes reproduce linear growth, transition to turbulence, and the practically important effects of mixing. Now we offer a family of unstable solutions featuring all three elements relevant to magnetically driven implosions: convergent flow, magnetic field, and a shock wave.

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A. Beresnyak, A. Velikovich, J. Giuliani, et. al.
Wed, 22 Dec 21
4/67

Comments: 24 pages, 9 figures, submitted to JFM

Non-Gaussian generalization of the Kazantsev-Kraichnan model [CL]

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http://arxiv.org/abs/2112.05738


We consider a natural generalization of the Kazantsev-Kraichnan model for small-scale turbulent dynamo. This generalization takes account of statistical time asymmetry of a turbulent flow, and, thus, allows to describe velocity fields with energy cascade. For three-dimensional velocity field, generalized Kazantsev equation is derived, and evolution of the second order magnetic field correlator is investigated for large but finite magnetic Prandtl numbers. It is shown that as $Pr_m \to \infty$, the growth increment tends to the limit known from the T-exponential (Lagrangian deformation) method. Magnetic field generation is shown to be weaker than that in the Gaussian velocity field for any direction of the energy cascade, and depends essentially on the Prandtl number.

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A. Kopyev, A. Kiselev, A. Il’yn, et. al.
Mon, 13 Dec 21
7/70

Comments: 6 figures, 1 table

Magnetic energy spectrum produced by turbulent dynamo: effect of time irreversibility [CL]

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http://arxiv.org/abs/2112.05736


We consider the kinematic stage of evolution of magnetic field advected by turbulent hydrodynamic flow. We use a generalization of the Kazantsev-Kraichnan model to investigate time irreversible flows. In the viscous range of scales, the infinite-time limit of the spectrum is a power law but its slope is more flat than that predicted by Kazantsev model. This result agrees with numerical simulations. At early stages, the rate of magnetic energy growth is slower than that in the time-symmetric case. We show that for high magnetic Prandtl turbulent plasma, the formation of the spectrum shape takes very long time and may never happen because of the nonlinearity. A finite-time ansatz for the spectrum shape more accurate than a power law is proposed.

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A. Kopyev, A. Il’yn, V. Sirota, et. al.
Mon, 13 Dec 21
51/70

Comments: N/A

Exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence: a link between fluid cascade and instabilities [CL]

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http://arxiv.org/abs/2112.03601


We derive a first exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence. For a gyrotropic pressure tensor, we study the double-adiabatic case and show the presence of new flux and source terms in the exact law, reminiscent of the firehose and mirror instabilities. The Hall term is shown to bring ion-scale corrections to the exact law without affecting explicitly the pressure terms. In the pressure isotropy limit we recover all known results obtained for isothermal and polytropic closures. The incompressible limit of the gyrotropic system leads to a generalization of the Politano and Pouquet’s law where a new incompressible source term is revealed and reflects exchanges of the magnetic and kinetic energies with the no-longer-conserved internal energy. We highlight the possibilities offered by the new laws to investigate potential links between turbulence cascade and instabilities widely observed in laboratory and astrophysical plasmas.

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P. Simon and F. Sahraoui
Wed, 8 Dec 21
14/77

Comments: 8 pages. Submitted

On the stability of isothermal shocks in black hole accretion disks [HEAP]

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http://arxiv.org/abs/2112.01665


Most black holes possess accretion disks. Models of such disks inform observations and constrain the properties of the black holes and their surrounding medium. Here, we study isothermal shocks in a thin black hole accretion flow. Modelling infinitesimal molecular viscosity allows the use of multiple-scales matched asymptotic methods. We thus derive the first explicit calculations of isothermal shock stability. We find that the inner shock is always unstable, and the outer shock is always stable. The growth/decay rates of perturbations depend only on an effective potential and the incoming–outgoing flow difference at the shock location. We give a prescription of accretion regimes in terms of angular momentum and black hole radius. Accounting for angular momentum dissipation implies unstable outer shocks in much of parameter space, even for realistic viscous Reynolds numbers of the order $\approx 10^{20}$.

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E. Hester, G. Vasil and M. Wechselberger
Mon, 6 Dec 21
28/61

Comments: 26 pages

From helical to standard magnetorotational instability: predictions for upcoming liquid sodium experiments [CL]

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http://arxiv.org/abs/2112.01399


We conduct a linear analysis of axisymmetric magnetorotational instability (MRI) in a magnetized cylindrical Taylor-Couette (TC) flow for its standard version (SMRI) with a purely axial background magnetic field and two further types — helically modified SMRI (H-SMRI) and helical MRI (HMRI) — in the presence of combined axial and azimuthal magnetic fields. This study is intended as preparatory for upcoming large-scale liquid sodium MRI experiments planned within the DRESDYN project at Helmholtz-Zentrum Dresden-Rossendorf, so we explore these instability types for typical values of the main parameters: the magnetic Reynolds number, the Lundquist number and the ratio of the angular velocities of the cylinders, which are attainable in these experiments. In contrast to previous attempts of detecting MRI in the lab, our results demonstrate that SMRI and its helically modified version can in principle be detectable in the DRESDYN-TC device for the range of the above parameters, including the astrophysically most important Keplerian rotation, despite the extremely small magnetic Prandtl number of liquid sodium. Since in the experiments we plan to approach (H-)SMRI from the previously studied HMRI regime, we characterize the continuous and monotonous transition between the both regimes. We show that H-SMRI, like HMRI, represents an overstability (travelling wave) with non-zero frequency linearly increasing with azimuthal field. Because of its relevance to finite size flow systems in experiments, we also analyze the absolute form of H-SMRI and compare its growth rate and onset criterion with the convective one.

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A. Mishra, G. Mamatsashvili and F. Stefani
Fri, 3 Dec 21
61/81

Comments: 16 pages, 13 figures, submitted to Physical Review Fluids

Polytropic Wind Solutions via the Complex Plane Strategy [SSA]

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http://arxiv.org/abs/2111.14150


Solar-type stars generate spherical winds, which are pressure driven flows, that start subsonic, reach the sound speed at the sonic point and transition to supersonic flows. The sonic point, mathematically corresponds to a singularity of the system of differential equations describing the flow. In the problem of an isothermal wind, the Parker solution provides an exact analytical expression tuned appropriately so that the singularity does not affect the solution. However, if the wind is polytropic it is not possible to find an analytical solution and a numerical approach needs to be followed. We study solutions of spherical winds that are driven by pressure within a gravitational field. The solutions pass smoothly from the critical point and allow us to study the impact of the changes of the polytropic index to these winds. We explore the properties of these solutions as a function of the polytropic index and the boundary conditions used. We apply the Complex Plane Strategy (CPS) and we obtain numerically solutions of polytropic winds. This allows us to avoid the singularity appearing in the equations through the introduction complex variables and integration on the complex plane. Applying this method, we obtain solutions with physical behaviour at the stellar surface, the sonic point and at large distances from the star. We further explore the role of the polytropic index in the flow and the effect of mass–loss rate and temperature on the solution. We find that the increase of polytropic index as well as the decrease of flow parameter both yield to a smoother velocity profile and lower velocities and shifts the transition point from subsonic to supersonic behaviour further from the star. Finally, we verify that the increasing of coronal temperature yields higher wind velocities and a weaker dependence on polytropic index.

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V. Karageorgopoulos, K. Gourgouliatos and V. Geroyannis
Tue, 30 Nov 21
70/105

Comments: Article history to Astronomy and Computing: Submitted 26 December 2020, Accepted 5 August 2021, Available online 11 August 2021

Impact of anti-solar differential rotation in mean-field solar-type dynamos — Exploring possible magnetic cycles in slowly rotating stars [SSA]

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http://arxiv.org/abs/2111.12722


Over the course of their lifetimes, the rotation of solar-type stars goes through different phases. Once they reach the zero-age main sequence (ZAMS), their global rotation rate decreases during the main sequence until at least the solar age, approximately following the empirical Skumanich law and enabling gyrochronology. Older solar-type stars might then reach a point of transition when they stop braking, according to recent results of asteroseismology. Additionally, recent 3D numerical simulations of solar-type stars show that different regimes of differential rotation can be characterized with the Rossby number. In particular, anti-solar differential rotation (fast poles, slow equator) may exist for high Rossby number (slow rotators). If this regime occurs during the main sequence and, in general, for slow rotators, we may consider how magnetic generation through the dynamo process might be impacted. In particular, we consider whether slowly rotating stars are indeed subject to magnetic cycles.
We find that kinematic $\alpha$ $\Omega$ dynamos allow for the presence of magnetic cycles and global polarity reversals for both rotation regimes, but only if the $\alpha$-effect is saddled on the tachocline. If it is distributed in the convection zone, solar-type cases still possess a cycle and anti-solar cases do not. Conversely, we have not found any possibility for sustaining a magnetic cycle with the traditional Babcock-Leighton flux-transport dynamos in the anti-solar differential rotation regime due to flux addition. Graphic interpretations are proposed in order to illustrate these cases. However, we find that hybrid models containing both prescriptions can still sustain local polarity reversals at some latitudes.
We conclude that stars in the anti-solar differential rotation regime can sustain magnetic cycles only for very specific dynamo processes.

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Q. Noraz, A. Brun, A. Strugarek, et. al.
Mon, 29 Nov 21
63/94

Comments: 18 pages and 16 Figures

A Conservative Finite Element Solver for MHD Kinematics equations: Vector Potential method and Constraint Preconditioning [CL]

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http://arxiv.org/abs/2111.11693


A new conservative finite element solver for the three-dimensional steady magnetohydrodynamic (MHD) kinematics equations is presented.The solver utilizes magnetic vector potential and current density as solution variables, which are discretized by H(curl)-conforming edge-element and H(div)-conforming face element respectively. As a result, the divergence-free constraints of discrete current density and magnetic induction are both satisfied. Moreover the solutions also preserve the total magnetic helicity. The generated linear algebraic equation is a typical dual saddle-point problem that is ill-conditioned and indefinite. To efficiently solve it, we develop a block preconditioner based on constraint preconditioning framework and devise a preconditioned FGMRES solver. Numerical experiments verify the conservative properties, the convergence rate of the discrete solutions and the robustness of the preconditioner.

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X. Li and L. Li
Wed, 24 Nov 21
6/61

Comments: 13 pages. arXiv admin note: text overlap with arXiv:1712.08922

The stress-pressure lag in MRI turbulence and its implications for thermal instability in accretion discs [HEAP]

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http://arxiv.org/abs/2111.11226


The classical alpha-disc model assumes that the turbulent stress scales linearly with — and responds instantaneously to — the pressure. It is likely, however, that the stress possesses a non-negligible relaxation time and will lag behind the pressure on some timescale. To measure the size of this lag we carry out unstratified 3D magnetohydrodynamic shearing box simulations with zero-net-magnetic-flux using the finite-volume code PLUTO. We impose thermal oscillations of varying periods via a cooling term, which in turn drives oscillations in the turbulent stress. Our simulations reveal that the stress oscillations lag behind the pressure by $\sim 5$ orbits in cases where the oscillation period is several tens of orbits or more. We discuss the implication of our results for thermal and viscous overstability in discs around compact objects.

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L. Held and H. Latter
Tue, 23 Nov 21
53/84

Comments: Accepted for publication in MNRAS (8 pages, 7 figures)

On the Conservation of Turbulence Energy in Turbulence Transport Models [CL]

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http://arxiv.org/abs/2111.11096


Zank et al. developed models describing the transport of low frequency incompressible and nearly incompressible turbulence in inhomogeneous flows. The formalism was based on expressing the fluctuating variables in terms of the Els\”assar variables and then taking “moments” subject to various closure hypotheses. The turbulence transport models are different according to whether the plasma beta regime is large or of order 1 or smaller. Here, we show explicitly that the two sets of turbulence transport models admit a conservation representation that resembles the well-known WKB transport equation for Alfv\’en wave energy density after introducing appropriate definitions of the “pressure” associated with the turbulent fluctuations. This includes introducing a distinct turbulent pressure tensor for 3D incompressible turbulence (the large plasma beta limit) and pressure tensors for quasi-2D and slab turbulence (the plasma beta order 1 or small regimes) that generalize the form of the WKB pressure tensor. Various limits of the different turbulent pressure tensors are discussed. However, the analogy between the conservation form of the turbulence transport models and the WKB model is not close for multiple reasons, including that the turbulence models express fully nonlinear physical processes unlike the strictly linear WKB description. The analysis presented here serves both as a check on the validity and correctness of the turbulence transport models and provides greater transparency of the energy dissipation term and the “turbulent pressure” in our models, which is important for many practical applications.

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B. Wang, G. Zank, L. Adhikari, et. al.
Tue, 23 Nov 21
75/84

Comments: 19 pages, 0 figure

Modelling stellar convective transport with plumes: I. Non-equilibrium turbulence effect in double-averaging formulation [SSA]

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http://arxiv.org/abs/2111.08921


Plumes in a convective flow, whose flow structure is localised in space and time, are considered to be relevant to the turbulent transport in convection. The effective mass, momentum, and heat transports in the convective turbulence are investigated in the framework of time–space double averaging procedure, where a field quantity is decomposed into three parts: the spatiotemporal mean (spatial average of the time-averaged) field, the dispersion or coherent fluctuation (deviation from the spatiotemporal mean), and the random or incoherent fluctuation. With this double-averaging framework, turbulent correlations such as the Reynolds stress, turbulent mass flux, turbulent internal-energy flux, etc., in the mean-field equations are divided into the dispersion/coherent correlation part and the random/incoherent correlation part. The evolution equations of these two parts of the correlation show what are responsible for the conversion of the fluctuation energy between the coherent and incoherent components. By reckoning the plume as the coherent fluctuation, a transport model for the convective turbulence is constructed with the aid of the non-equilibrium effect along plume motions, and applied to a stellar convective flow. One of the prominent characteristics of a surface cooling-driven convection, the enhanced and localised turbulent mass flux below the surface layer, which cannot be reproduced at all by the usual eddy-diffusivity model with mixing length theory (MLT), is well reproduced by the present model with the non-equilibrium effect. Our results show that the incorporation of plume motion into turbulent transport model through the non-equilibrium effect is an important and very relevant extension of mean-field theory beyond the heuristic gradient transport model with MLT.

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N. Yokoi, Y. Masada and T. Takiwaki
Thu, 18 Nov 21
17/92

Comments: 18 pages, 8 figures

Hydrodynamical transport of angular momentum in accretion disks in the presence of nonlinear perturbations due to noise [HEAP]

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http://arxiv.org/abs/2111.08724


The origin of hydrodynamical instability and turbulence in the Keplerian accretion disk is a long-standing puzzle. The flow therein is linearly stable. Here we explore the evolution of perturbation in this flow in the presence of an additional force. Such a force, which is expected to be stochastic in nature hence behaving as noise, could result from thermal fluctuations (however small be), grain-fluid interactions, feedback from outflows in astrophysical disks, etc. We essentially establish the evolution of nonlinear perturbation in the presence of Coriolis and external forces, which is the modified Landau equation. We obtain that even in the linear regime, under suitable forcing and Reynolds number, the otherwise least stable perturbation evolves to a very large saturated amplitude, leading to nonlinearity and plausible turbulence. Hence, forcing essentially leads a linear stable mode to unstable. We further show that nonlinear perturbation diverges at a shorter time-scale in the presence of force, leading to a fast transition to turbulence. Interestingly, the emergence of nonlinearity depends only on the force but not on the initial amplitude of perturbation, unlike the original Landau equation-based solution.

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S. Ghosh and B. Mukhopadhyay
Thu, 18 Nov 21
57/92

Comments: 12 pages including 6 figures. Based on the talk given in the parallel session “Accretion Discs and Jets” in the Sixteenth Marcel Grossmann Meeting held online during July 5-10, 2021; to appear in the proceedings of the Sixteenth Marcel Grossmann Meeting

MRI-driven $α-Ω$ dynamos in protoneutron stars [HEAP]

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http://arxiv.org/abs/2111.02148


Magnetars are highly magnetized neutron stars that can produce X-ray and soft gamma-ray emissions and that have a dipole of $10^{14}$ G to $10^{15}$ G. A promising mechanism to explain magnetar formation is magnetic field amplification by the MRI in fast-rotating protoneutron stars (PNS). This scenario is supported by recent global models showing that small-scale turbulence can generate a dipole with magnetar-like intensity. However, the impact of buoyancy and density stratification on the efficiency of the MRI at generating a dipole is still unknown. We assess the impact of the density and entropy profiles on the MRI dynamo in a global model of a fast-rotating PNS, which focuses on its outer stratified region stable to convection. Using the pseudo-spectral code MagIC, we perform three-dimensional Boussinesq and anelastic MHD simulations in spherical geometry with explicit diffusivities. We perform a parameter study in which we investigate the effect of different approximations and of thermal diffusion. We obtain a self-sustained turbulent MRI-driven dynamo, which confirms most of our previous incompressible results once rescaled for density. The MRI also generates a non-dominant equatorial dipole, which represents about 4.3% of the averaged magnetic field strength. Interestingly, in the presence of a density gradient, an axisymmetric magnetic field at large scales oscillates with time, which can be described as a mean-field $\alpha-\Omega$ dynamo. Buoyancy damps turbulence in the equatorial plane but it has overall a relatively weak influence with a realistic high thermal diffusion. Our results support the ability of the MRI to generate magnetar-like large-scale magnetic fields. They furthermore predict the presence of an $\alpha-\Omega$ dynamo in the protoneutron star, which could be important to model in-situ magnetic field amplification in core-collapse supernovae. [abridged]

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A. Reboul-Salze, J. Guilet, R. Raynaud, et. al.
Thu, 4 Nov 21
35/73

Comments: Submitted to A&A, 20 pages, 19 figures

Dynamics in a stellar convective layer and at its boundary: Comparison of five 3D hydrodynamics codes [SSA]

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http://arxiv.org/abs/2111.01165


Our ability to predict the structure and evolution of stars is in part limited by complex, 3D hydrodynamic processes such as convective boundary mixing. Hydrodynamic simulations help us understand the dynamics of stellar convection and convective boundaries. However, the codes used to compute such simulations are usually tested on extremely simple problems and the reliability and reproducibility of their predictions for turbulent flows is unclear. We define a test problem involving turbulent convection in a plane-parallel box, which leads to mass entrainment from, and internal-wave generation in, a stably stratified layer. We compare the outputs from the codes FLASH, MUSIC, PPMSTAR, PROMPI, and SLH, which have been widely employed to study hydrodynamic problems in stellar interiors. The convection is dominated by the largest scales that fit into the simulation box. All time-averaged profiles of velocity components, fluctuation amplitudes, and fluxes of enthalpy and kinetic energy are within $\lesssim 3\sigma$ of the mean of all simulations on a given grid ($128^3$ and $256^3$ grid cells), where $\sigma$ describes the statistical variation due to the flow’s time dependence. They also agree well with a $512^3$ reference run. The $128^3$ and $256^3$ simulations agree within $9\%$ and $4\%$, respectively, on the total mass entrained into the convective layer. The entrainment rate appears to be set by the amount of energy that can be converted to work in our setup and details of the small-scale flows in the boundary layer seem to be largely irrelevant. Our results lend credence to hydrodynamic simulations of flows in stellar interiors. We provide in electronic form all outputs of our simulations as well as all information needed to reproduce or extend our study.

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R. Andrassy, J. Higl, H. Mao, et. al.
Wed, 3 Nov 21
29/106

Comments: 20 pages, 18 figures, submitted to A&A

Acceleration and clustering of cosmic dust in a gravoturbulent gas — I. Numerical simulation of the nearly Jeans-unstable case [GA]

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http://arxiv.org/abs/2111.01289


We investigate the dynamics of interstellar dust particles in moderately high resolution ($512^3$ grid points) simulations of forced compressible transonic turbulence including self-gravity of the gas. Turbulence is induced by stochastic compressive forcing which is delta-correlated in time. By considering the nearly Jeans-unstable case, where the scaling of the simulation is such that a statistical steady state without any irreversible collapses is obtained, we obtain a randomly varying potential, acting as a second stochastic forcing. We show that, in this setting, low-inertia grains follow the gas flow and cluster in much the same way as in a case of statistical steady-state turbulence without self-gravity. Large, high-inertia grains, however, are accelerated to much higher mean velocities in the presence of self-gravity. Grains of intermediate size also show an increased degree of clustering. We conclude that self-gravity effects can play an important role for aggregation/coagulation of dust even in a turbulent system which is not Jeans-unstable. In particular, the collision rate of large grains in the interstellar medium can be much higher than predicted by previous work.

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L. Mattsson and R. Hedvall
Wed, 3 Nov 21
34/106

Comments: 17 pages, 11 figures, accepted for publication MNRAS

Stellar convective penetration: parameterized theory and dynamical simulations [SSA]

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http://arxiv.org/abs/2110.11356


Most stars host convection zones in which heat is transported directly by fluid motion. Parameterizations like mixing length theory adequately describe convective flows in the bulk of these regions, but the behavior of convective boundaries is not well understood. Here we present 3D numerical simulations which exhibit penetration zones: regions where the entire luminosity could be carried by radiation, but where the temperature gradient is approximately adiabatic and convection is present. To parameterize this effect, we define the “penetration parameter” $\mathcal{P}$ which compares how far the radiative gradient deviates from the adiabatic gradient on either side of the Schwarzschild convective boundary. Following Roxburgh (1989) and Zahn (1991), we construct an energy-based theoretical model in which the extent of penetration is controlled by $\mathcal{P}$. We test this theory using 3D numerical simulations which employ a simplified Boussinesq model of stellar convection. We find significant convective penetration in all simulations. Our simple theory describes the simulations well. Penetration zones can take thousands of overturn times to develop, so long simulations or accelerated evolutionary techniques are required. In stellar contexts, we expect $\mathcal{P} \approx 1$ and in this regime our results suggest that convection zones may extend beyond the Schwarzschild boundary by up to $\sim$20-30\% of a mixing length. We present a MESA stellar model of the Sun which employs our parameterization of convective penetration as a proof of concept. We discuss prospects for extending these results to more realistic stellar contexts.

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E. Anders, A. Jermyn, D. Lecoanet, et. al.
Mon, 25 Oct 21
29/76

Comments: Supplemental materials available at this https URL

The Acoustic Resonant Drag Instability with a Spectrum of Grain Sizes [GA]

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http://arxiv.org/abs/2110.11422


We study the linear growth and nonlinear saturation of the “acoustic Resonant Drag Instability” (RDI) when the dust grains, which drive the instability, have a wide, continuous spectrum of different sizes. This physics is generally applicable to dusty winds driven by radiation pressure, such as occurs around red-giant stars, star-forming regions, or active galactic nuclei. Depending on the physical size of the grains compared to the wavelength of the radiation field that drives the wind, two qualitatively different regimes emerge. In the case of grains that are larger than the radiation’s wavelength — termed the constant-drift regime — the grain’s equilibrium drift velocity through the gas is approximately independent of grain size, leading to strong correlations between differently sized grains that persist well into the saturated nonlinear turbulence. For grains that are smaller than the radiation’s wavelength — termed the non-constant-drift regime — the linear instability grows more slowly than the single-grain-size RDI and only the larger grains exhibit RDI-like behavior in the saturated state. A detailed study of grain clumping and grain-grain collisions shows that outflows in the constant-drift regime may be effective sites for grain growth through collisions, with large collision rates but low collision velocities.

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J. Squire, S. Moroianu and P. Hopkins
Mon, 25 Oct 21
61/76

Comments: N/A

Chirality in Astrophysics [SSA]

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http://arxiv.org/abs/2110.08117


Chirality, or handedness, enters astrophysics in three distinct ways. Magnetic field and vortex lines tend to be helical and have a systematic twist in the northern and southern hemispheres of a star or a galaxy. Helicity is here driven by external factors. Chirality can also enter at the microphysical level and can then be traced back to the parity-breaking weak force. Finally, chirality can arise spontaneously, but this requires not only the presence of an instability, but also the action of nonlinearity. Examples can be found both in magnetohydrodynamics and in astrobiology, where homochirality among biomolecules probably got established at the origin of life. In this review, all three types of chirality production will be explored and compared.

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A. Brandenburg
Mon, 18 Oct 21
39/68

Comments: 20 pages, 6 figures, 1 table, to appear in the proceedings to Nobel Symposium 167: Chiral Matter, eds. E. Babaev, D. Kharzeev, M. Larsson, A. Molochkov, & V. Zhaunerchyk, World Scientific, in press

Rossby numbers and stiffness values inferred from gravity-mode asteroseismology of rotating F- and B-type dwarfs: consequences for mixing, transport, magnetism, and convective penetration [SSA]

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http://arxiv.org/abs/2110.06220


Multi-dimensional (magneto-)hydrodynamical simulations of physical processes in stellar interiors depend on a multitude of uncalibrated free parameters, which set the spatial and time scales of their computations. We aim to provide an asteroseismic calibration of the wave and convective Rossby numbers, and of the stiffness at the interface between the convective core and radiative envelope of intermediate-mass stars. We deduce these quantities for rotating dwarfs from the observed properties of their identified gravity and gravito-inertial modes. We rely on near-core rotation rates and asteroseismic models of 26 B- and 37 F-type dwarf pulsators derived from 4-year Kepler space photometry, high-resolution spectroscopy and Gaia astrometry in the literature to deduce their convective and wave Rossby numbers. We compute the stiffness at the convection/radiation interface from the inferred maximum buoyancy frequency at the interface and the convective turnover frequency in the core. We use those asteroseismically inferred quantities to make predictions of convective penetration levels, local flux levels of gravito-inertial waves triggered by the convective core, and of the cores’ potential rotational and magnetic states. Our sample of 63 gravito-inertial mode pulsators covers near-core rotation rates from almost zero up to the critical rate. The frequencies of their identified modes lead to models with stiffness values between $10^{2.69}$ and $10^{3.60}$ for the B-type pulsators, while those of F-type stars cover the range from $10^{3.47}$ to $10^{4.52}$. The convective Rossby numbers derived from the maximum convective diffusion coefficient in the convective core, based on mixing length theory and a value of the mixing length coefficient relevant for these pulsators, vary between $10^{-2.3}$ and $10^{-0.8}$ for B-type stars and $10^{-3}$ and $10^{-1.5}$ for F-type stars. (abridged)

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C. Aerts, K. Augustson, S. Mathis, et. al.
Thu, 14 Oct 21
40/62

Comments: 10 pages, 8 figures, accepted for publication in Astronomy & Astrophysics

Extending Israel and Stewart hydrodynamics to relativistic superfluids via Carter's multifluid approach [CL]

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http://arxiv.org/abs/2110.05546


We construct a relativistic model for bulk viscosity and heat conduction in a superfluid. Building on the principles of Unified Extended Irreversible Thermodynamics, the model is derived from Carter’s multifluid approach for a theory with three currents, where the quasi-particle current is an independent hydrodynamic degree of freedom. For small deviations from local thermodynamic equilibrium, the model reduces to an extension of the Israel-Stewart theory to superfluid systems. It can, therefore, be made hyperbolic, causal and stable if the microscopic input is accurate. The non-dissipative limit of the model is the relativistic two-fluid model of Carter, Khalatnikov and Gusakov. The Newtonian limit of the model is an Extended-Irreversible-Thermodynamic extension of Landau’s two-fluid model. The model predicts the existence of four bulk viscosity coefficients and accounts for their microscopic origin, providing their exact formulas in terms of the quasi-particle creation rate. Furthermore, when fast oscillations of small amplitude around the equilibrium are considered, the relaxation-time term in the telegraph-type equations for the bulk viscosities accounts directly for their expected dependence on the frequency.

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L. Gavassino, M. Antonelli and B. Haskell
Wed, 13 Oct 21
54/80

Comments: 33 pages, 0 figures. Comments welcome

On the dynamics of overshooting convection in spherical shells: Effect of density stratification and rotation [SSA]

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http://arxiv.org/abs/2110.05432


Overshooting of turbulent motions from convective regions into adjacent stably stratified zones plays a significant role in stellar interior dynamics as this process may lead to mixing of chemical species, and contribute to the transport of angular momentum and magnetic fields. We present a series of fully non-linear, three-dimensional (3D) anelastic simulations of overshooting convection in a spherical shell which are focused on the dependence of the overshooting dynamics on the density stratification and the rotation, both key ingredients in stars which however have not been studied systematically together via global simulations. We demonstrate that the overshoot lengthscale is not simply a monotonic function of the density stratification in the convective region but instead, it depends on the ratio of the density stratifications in the two zones. Additionally, we find that the overshoot lengthscale decreases with decreasing Rossby number Ro and scales as Ro$^{0.23}$ while it also depends on latitude with higher Rossby cases leading to a weaker latitudinal variation. We examine the mean flows arising due to rotation and find that they extend beyond the base of the convection zone into the stable region. Our findings may provide a better understanding of the dynamical interaction between stellar convective and radiative regions, and motivate future studies particularly related to the solar tachocline and the implications of its overlapping with the overshoot region.

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L. Korre and N. Featherstone
Tue, 12 Oct 21
50/73

Comments: Accepted to ApJ

The maximum entropy distributions of collisionless particle velocity, speed, and energy for statistical mechanics of self-gravitating collisionless flow (SG-CFD) [CEA]

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http://arxiv.org/abs/2110.03126


The halo-mediated inverse mass cascade is a key feature of the intermediate statistically steady state for self-gravitating collisionless flow (SG-CFD). How the inverse mass cascade maximizes system entropy and develops limiting velocity/energy distributions are fundamental questions to answer. We present a statistical theory concerning the maximum entropy distributions of particle velocity, speed, and energy for self-gravitating systems involving a power-law long-range interaction with an arbitrary exponent $n$. For system with long-range interaction ($-2<n<0$), a broad spectrum of halos and halo groups are necessary to form from inverse mass cascade to maximize the system entropy. While particle velocity in each halo group is still Gaussian, the velocity distribution of entire system can be non-Gaussian. With the virial equilibrium for local mechanical equilibrium of halo groups, the maximum entropy principle is applied for statistical equilibrium of global system to derive the limiting distributions. Halo mass function is not required in this formulation, but it is a direct result of entropy maximization. The predicted velocity distribution involves a shape parameter $\alpha$ that is dependent on the exponent $n$. The velocity distribution approaches Laplacian with $\alpha\rightarrow0$ and Gaussian with $\alpha\rightarrow\infty$. For intermediate $\alpha$, the maximum entropy distribution naturally exhibits a Gaussian core at small velocity and exponential wings at large velocity. The total energy of collisionless particles at a given speed follows a parabolic scaling for small speed ($\epsilon \propto v^2$) and a linear scaling ($\epsilon \propto v$) for large speed. Results are compared against a N-body simulation with good agreement.

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Z. Xu
Fri, 8 Oct 21
29/70

Comments: 7 Figures, 2 Tables

The traditional approximation of rotation for rapidly rotating stars and planets. II. Deformation and differential rotation [SSA]

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http://arxiv.org/abs/2110.03619


We examine the dynamics of low-frequency gravito-inertial waves (GIWs) in differentially rotating deformed radiation zones in stars and planets by generalising the traditional approximation of rotation (TAR). The TAR treatment was built on the assumptions that the star is spherical and uniformly rotating. However, it has been generalised in our previous work by including the effects of the centrifugal deformation using a non-perturbative approach in the uniformly rotating case. We aim to carry out a new generalisation of the TAR treatment to account for the differential rotation and the strong centrifugal deformation simultaneously. We generalise our previous work by taking into account the differential rotation in the derivation of our complete analytical formalism that allows the study of the dynamics of GIWs in differentially and rapidly rotating stars. We derived the complete set of equations that generalises the TAR, simultaneously taking the full centrifugal acceleration and the differential rotation into account. Within the validity domain of the TAR, we derived a generalised Laplace tidal equation for the horizontal eigenfunctions and asymptotic wave periods of the GIWs, which can be used to probe the structure and dynamics of differentially rotating deformed stars with asteroseismology. A new generalisation of the TAR, which simultaneously takes into account the differential rotation and the centrifugal acceleration in a non-perturbative way, was derived. This generalisation allowed us to study the detectability and the signature of the differential rotation on GIWs in rapidly rotating deformed stars and planets. We found that the effects of the differential rotation in early-type deformed stars on GIWs is theoretically largely detectable in modern space photometry using observations from $\textit{Kepler}$ and TESS.

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H. Dhouib, V. Prat, T. Reeth, et. al.
Fri, 8 Oct 21
67/70

Comments: 13 pages, 11 figures, 1 table, abstract shortened for arXiv. Accepted for publication in A&A. arXiv admin note: substantial text overlap with arXiv:2104.09302

On the toroidal-velocity anti-dynamo theorem under the presence of nonuniform electric conductivity [CL]

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http://arxiv.org/abs/2110.02309


Laminar electrically conducting Couette flows with quasi-Keplerian rotation law and nonuniform conductivity are probed for dynamo instability. In spherical geometry the equations for the poloidal and the toroidal field components completely decouple resulting in free decay independent of the spatial distribution of the electric conductivity. For cylindric flows the decoupling vanishes but also here we do not find dynamo excitations for the two cases that the electric conductivity only depends on the radius or — much more complex — that it only depends on the azimuth. The transformation of the plane-flow dynamo model of Busse & Wicht (1992) to cylindric or spherical geometry, therefore, fails. It is also shown that even the inclusion of axial flows of both signs does not support the dynamo mechanism. The Elsasser toroidal-velocity antidynamo theorem, after which dynamos without any radial velocity component cannot work, is thus not softed by nonuniform conductivity distributions.

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G. Rüdiger and M. Schultz
Thu, 7 Oct 21
12/51

Comments: 8 pages, 6 figures

Magnetopause ripples going against the flow form azimuthally stationary surface waves [CL]

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http://arxiv.org/abs/2110.02681


Surface waves process the turbulent disturbances which drive dynamics in many space, astrophysical and laboratory plasma systems, with the outer boundary of Earth’s magnetosphere, the magnetopause, providing an accessible environment to study them. Like waves on water, magnetopause surface waves are thought to travel in the direction of the driving solar wind, hence a paradigm in global magnetospheric dynamics of tailward propagation has been well-established. Here we show through multi-spacecraft observations, global simulations, and analytic theory that the lowest-frequency impulsively-excited magnetopause surface waves, with standing structure along the terrestrial magnetic field, propagate against the flow outside the boundary. Across a wide local time range (09-15h) the waves’ Poynting flux exactly balances the flow’s advective effect, leading to no net energy flux and thus stationary structure across the field also. Further down the equatorial flanks, however, advection dominates hence the waves travel downtail, seeding fluctuations at the resonant frequency which subsequently grow in amplitude via the Kelvin-Helmholtz instability and couple to magnetospheric body waves. This global response, contrary to the accepted paradigm, has implications on radiation belt, ionospheric, and auroral dynamics and potential applications to other dynamical systems.

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M. Archer, M. Hartinger, F. Plaschke, et. al.
Thu, 7 Oct 21
20/51

Comments: N/A

Turbulence-induced transport dynamo mechanism [CL]

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http://arxiv.org/abs/2110.02433


The transport dynamo mechanism, which describes the magnetic field generation by diffusion flow is reviewed. In this mechanism, the cross-field transport caused by the random motion of fluid breaks the frozen-flux approximation, and the resulting cross-field diffusion that can generate the magnetic field. Turbulence can play an important role in inducing such random motion. Compared to the conventional dynamo mechanism, this transport mechanism has several special features that the field generation can occur on a very slow time scale because the mechanism is mediated by diffusion and that this mechanism is practically meaningful only when there is density inhomogeneity. Turbulence can significantly enhance cross-field diffusion far beyond collisional transport. The physical meanings of the diffusion-generated magnetic fields are discussed in detail.

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C. Ryu
Thu, 7 Oct 21
29/51

Comments: 13 pages,2 figures

Turbulent cascade and energy transfer rate in a solar coronal mass ejection [SSA]

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http://arxiv.org/abs/2110.02664


Turbulence properties are examined before, during and after a coronal mass ejection (CME) detected by the6Wind spacecraft on July 2012. The power-law scaling of the structure functions, providing information on the7power spectral density and flatness of the velocity, magnetic filed and density fluctuations, were examined. The8third-order moment scaling law for incompressible, isotropic magnetohydrodynamic turbulence was observed9in the preceding and trailing solar wind, as well as in the CME sheath and magnetic cloud. This suggests that10the turbulence could develop sufficiently after the shock, or that turbulence in the sheath and cloud regions11was robustly preserved even during the mixing with the solar wind plasma. The turbulent energy transfer rate12was thus evaluated in each of the regions. The CME sheath shows an increase of energy transfer rate, as13expected from the lower level of Alfv\’enic fluctuations and suggesting the role of the shock-wind interaction as14an additional source of energy for the turbulent cascade.

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L. Sorriso-Valvo, E. Yordanova, A. Dimmock, et. al.
Thu, 7 Oct 21
35/51

Comments: N/A

On the mode structure of imperfect fluids [CL]

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http://arxiv.org/abs/2110.00975


This paper tries to obtain a simple picture of several aspects of the mode structure in relativistic non-equilibrium thermodynamics. Its pedagogical focus is on the relation between long-wavelength perturbation modes of the causal M\”{u}ller-Israel-Stewart (MIS) theory and those of the traditional Eckart theory. Principally, this issue was clarified in a series of papers by Hiscock and Lindblom (see [8-10]). Here, I put together some essential features which do not require the entire formalism of the complete theory.

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W. Zimdahl
Wed, 6 Oct 21
38/56

Comments: 11 pages

Towards Adaptive Simulations of Dispersive Tsunami Propagation from an Asteroid Impact [CL]

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http://arxiv.org/abs/2110.01420


The long-term goal of this work is the development of high-fidelity simulation tools for dispersive tsunami propagation. A dispersive model is especially important for short wavelength phenomena such as an asteroid impact into the ocean, and is also important in modeling other events where the simpler shallow water equations are insufficient. Adaptive simulations are crucial to bridge the scales from deep ocean to inundation, but have difficulties with the implicit system of equations that results from dispersive models. We propose a fractional step scheme that advances the solution on separate patches with different spatial resolutions and time steps. We show a simulation with 7 levels of adaptive meshes and onshore inundation resulting from a simulated asteroid impact off the coast of Washington. Finally, we discuss a number of open research questions that need to be resolved for high quality simulations.

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M. Berger and R. LeVeque
Tue, 5 Oct 21
11/72

Comments: 16 pages, 5 figures, submitted to Proc. International Congress of Mathematicians, 2022

Large-scale Vortices in Rapidly Rotating Rayleigh-Bénard Convection at Small Prandtl number [CL]

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http://arxiv.org/abs/2109.14289


One prominent feature in the atmospheres of Jupiter and Saturn is the appearance of large-scale vortices. However, the sustaining mechanism of these large-scale vortices remains unclear. One possible mechanism is that these large-scale vortices are driven by rotating convection. Here we present numerical simulation results on rapidly rotating Rayleigh-B\’enard convection at a small Prandtl number $Pr=0.1$ (close to the turbulent Prandtl numbers of Jupiter and Saturn). We have identified four flow regimes in our simulation: multiple small vortices, coexisted large-scale cyclone and anticyclone, large-scale cyclone, and turbulence. The formation of large-scale vortices requires two conditions to be satisfied: the vertical Reynolds number is large ($Re_{z}\ge 400$), and the Rossby number is small ($Ro\leq 0.4$). Large-scale cyclone first appears when $Ro$ decreases to be smaller than 0.4. When $Ro$ further decreases to be smaller than 0.1, coexisted large-scale anticyclone emerges. We have studied the heat transfer in rapidly rotating convection. The result reveals that the heat transfer is more efficient in the anticyclonic region than in the cyclonic region. Besides, we find that 2D effect increases and 3D effect decreases in transporting convective flux as rotation rate increases. We find that aspect ratio has an effect on the critical Rossby number for the emergence of large-scale vortices. Our results provide helpful insights on understanding the dynamics of large-scale vortices in gas giants.

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T. Cai
Thu, 30 Sep 21
70/82

Comments: Accepted to ApJ

Evolution of primordial magnetic fields during large-scale structure formation [CEA]

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http://arxiv.org/abs/2109.13520


Primordial magnetic fields could explain the large-scale magnetic fields present in the Universe. Inflation and phase transitions in the early Universe could give rise to such fields with unique characteristics. We investigate the magneto-hydrodynamic evolution of these magnetogenesis scenarios with cosmological simulations. We evolve inflation-generated magnetic fields either as (i) uniform (homogeneous) or as (ii) scale-invariant stochastic fields, and phase transition-generated ones either as (iii) helical or as (iv) non-helical fields from the radiation-dominated epoch. We find that the final distribution of magnetic fields in the simulated cosmic web shows a dependence on the initial strength and the topology of the seed field. Thus, the observed field configuration retains information on the initial conditions at the moment of the field generation. If detected, primordial magnetic field observations would open a new window for indirect probes of the early universe. The differences between the competing models are revealed on the scale of galaxy clusters, bridges, as well as filaments and voids. The distinctive spectral evolution of different seed fields produces imprints on the correlation length today. We discuss how the differences between rotation measures from highly ionized regions can potentially be probed with forthcoming surveys.

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S. Mtchedlidze, P. Domínguez-Fernández, X. Du, et. al.
Wed, 29 Sep 21
31/78

Comments: 26 pages, 17 figures, comments welcome

Inverse mass cascade of self-gravitating collisionless flow and effects on halo deformation, energy, size, and density profiles [CEA]

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http://arxiv.org/abs/2109.12244


Inverse mass cascade is a key feature of the intermediate statistically steady state of self-gravitating collisionless flow (SG-CFD). This paper focus on the effects of mass cascade on halo energy, momentum, size, and density. Halo with fast mass accretion has an expanding core. Mass cascade forms a new layer of mass that deforms the original halo and induces nonzero radial flow (outwards for core and inwards for outer regions). The inward/outward flow leads to an extra length scale (scale radius) that is not present in isothermal profile. Halo concentration $c=3.5$ can be derived for fast growing halos. For cusp-core controversy, a double-power-law density is proposed as a result of radial flow. The inner/outer density are controlled by halo deformation rate and halo growth, respectively. The slower deformation at center, the steeper density. For fast growing halos, radial flow at center is simply Hubble flow that leads to the existence of central core. Mass cascade leads to nonzero halo surface energy/tension and radial flow that enhances the random motion in outer region. An effective exponent of gravity $n_e=-1.3$ (not -1) is obtained due to halo surface energy. Evolution of halo size follows geometric Brownian motion and lognormal distribution. The Brownian motion of particles in randomly evolving halos leads to Fokker-Planck equations for particle distribution that is related to radial and osmotic flow. Complete solutions of particle distribution are presented based on a simple model of osmotic flow. The proposed model agrees with simulation for a wide range of halo group sizes. With reference pressure/density defined at center, equation of state can be established for relative pressure/density. The center pressure, density, and dispersion are presented. The core size $x_c$ is obtained where Hubble flow is dominant. Simple closures are proposed for self-consistent halo density.

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Z. Xu
Tue, 28 Sep 21
66/89

Comments: N/A

Shock Physics in Warm Dense Matter–a quantum hydrodynamics perspective [CL]

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http://arxiv.org/abs/2109.09081


Warm dense matter (WDM)–an exotic, highly compressed state of matter between solid and plasma phases is of high current interest, in particular for astrophysics and inertial confinement fusion. For the latter, in particular the propagation of compression shocks is crucial. The main unknown in the shock propagation in WDM is the behavior of the electrons since they are governed by correlations, quantum and spin effects that need to be accounted for simultaneously. Here we describe the shock dynamics of the warm dense electron gas using a quantum hydrodynamic model. From the numerical hydrodynamic simulations we observe that the quantum Bohm pressure induces shear force which weakens the formation and strength of the shock. This is confirmed by the theoretical analysis of the early stage of the shock formation. Our theoretical and numerical analysis allows us to identify characteristic dimensionless shock propagation parameters at which the effect of the Bohm force is important.

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F. Graziani, Z. Moldabekov, B. Olson, et. al.
Tue, 21 Sep 21
72/85

Comments: N/A

Nonlinear simulations of tides in the convective envelopes of low-mass stars and giant gaseous planets [SSA]

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http://arxiv.org/abs/2109.08562


In close two-body astrophysical systems, such as binary stars or Hot Jupiter systems, tidal interactions often drive dynamical evolution on secular timescales. Many host stars and presumably giant gaseous planets feature a convective envelope. Tidal flows generated therein by the tidal potential of the companion can be dissipated through viscous friction, leading to the redistribution and exchange of angular momentum within the convective shell and with the companion, respectively. In the tightest systems, nonlinear effects are likely to have a significant impact on the tidal dissipation and trigger differential rotation in the form of zonal flows, as has been shown in previous studies. In this context, we investigate how the addition of nonlinearities affect the tidal flow properties, and energy and angular momentum balances, using 3D nonlinear simulations of an adiabatic and incompressible convective shell. In our study, we have chosen a body forcing where the equilibrium tide (the quasi-hydrostatic tidal flow component) acts via an effective forcing to excite tidal inertial waves in a spherical shell. Within this set-up, we show new results for the amplitude of the energy stored in zonal flows, angular momentum evolution, and its consequences on tidal dissipation in the envelopes of low-mass stars and giant gaseous planets.

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A. Astoul and A. Barker
Mon, 20 Sep 21
31/53

Comments: 4 pages, 2 figures, SF2A 2021 proceedings

Coupling between Turbulence and Solar-like Oscillations: a combined Lagrangian PDF/SPH approach. I — The stochastic wave equation [SSA]

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http://arxiv.org/abs/2109.05983


Aims. This series of papers aims at building a new formalism specifically tailored to study the impact of turbulence on the global modes of oscillation in solar-like stars. This first paper aims at deriving a linear wave equation that directly and consistently contains the turbulence as an input to the model, and therefore naturally contains the information on the coupling between the turbulence and the modes, through the stochasticity of the equations.
Methods. We use a Lagrangian stochastic model of turbulence based on Probability Density Function methods to describe the evolution of the properties of individual fluid particles through stochastic differential equations. We then transcribe these stochastic differential equations from a Lagrangian frame to an Eulerian frame, more adapted to the analysis of stellar oscillations. We combine this method with Smoothed Particle Hydrodynamics, where all the mean fields appearing in the Lagrangian stochastic model are estimated directly from the set of fluid particles themselves, through the use of a weighting kernel function allowing to filter the particles present in any given vicinity. The resulting stochastic differential equations on Eulerian variables are then linearised.
Results. We obtain a stochastic, linear wave equation governing the time evolution of the relevant wave variables, while at the same time containing the effect of turbulence. The wave equation generalises the classical, unperturbed propagation of acoustic waves in a stratified medium to a form that, by construction, accounts for the impact of turbulence on the mode in a consistent way. The effect of turbulence consists in a non-homogeneous forcing term, responsible for the stochastic driving of the mode, and a stochastic perturbation to the homogeneous part of the wave equation, responsible for both the damping of the mode and the modal surface effects.

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J. Philidet, K. Belkacem and M. Goupil
Tue, 14 Sep 21
54/88

Comments: Paper accepted for publication in A&A in this form. 18 pages (12 without Appendices), 1 figure

Turbulence in electromagnetically-driven Keplerian flows [CL]

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http://arxiv.org/abs/2109.05813


The flow of an electrically conducting fluid in a thin disc under the action of an azimuthal Lorentz force is studied experimentally. At small forcing, the Lorentz force is balanced by either viscosity or inertia, yielding quasi-Keplerian velocity profiles. For very large current and moderate magnetic field, we observe a new regime, fully turbulent, which exhibits large fluctuations and a Keplerian mean rotation profile $\Omega\sim \frac{\sqrt{IB}}{r^{3/2}}$. In this turbulent regime, the dynamics is typical of thin layer turbulence, characterized by a direct cascade of energy towards the small scales and an inverse cascade to large scale. Finally, at very large magnetic field, this turbulent flow bifurcates to a quasi-bidimensional turbulent flow involving the formation of a large scale condensate in the horizontal plane. These results are well understood as resulting from an instability of the B\”odewadt-Hartmann layers at large Reynolds number and discussed in the framework of similar astrophysical flows.

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M. Vernet, M. Pereira, S. Fauve, et. al.
Tue, 14 Sep 21
61/88

Comments: 30 pages, 12 figures

A Three Function Variational Principle for Stationary Non-Barotropic Magnetohydrodynamics [CL]

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http://arxiv.org/abs/2109.03817


Variational principles for magnetohydrodynamics (MHD) were in-troduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of non-barotropic stationary magnetohydrodynamics can be derived for certain field topologies.
The variational principle is given in terms of three independent functions for stationary non-barotropic flows.
This is a smaller number of variables than the eight variables which appear in the standard equations of non-barotropic magnetohydrodynamics which are the magnetic field $\vec B$ the velocity field $\vec v$, the entropy $s$ and the density $\rho$. We further investigate the case in the flow along magnetic lines is not ideal.

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A. Yahalom
Fri, 10 Sep 21
45/59

Comments: 30 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:2005.14005, arXiv:physics/0603115, arXiv:1510.00637, arXiv:1703.08072, arXiv:1801.06443, arXiv:physics/0603162

Kinematic dynamos in triaxial ellipsoids [EPA]

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http://arxiv.org/abs/2109.03232


Planetary magnetic fields are generated by motions of electrically conducting fluids in their interiors. The dynamo problem has thus received much attention in spherical geometries, even though planetary bodies are non-spherical. To go beyond the spherical assumption, we develop an algorithm that exploits a fully spectral description of the magnetic field in triaxial ellipsoids to solve the induction equation with local boundary conditions (i.e. pseudo-vacuum or perfectly conducting boundaries). We use the method to compute the free-decay magnetic modes and to solve the kinematic dynamo problem for prescribed flows. The new method is thoroughly compared with analytical solutions and standard finite-element computations, which are also used to model an insulating exterior. We obtain dynamo magnetic fields at low magnetic Reynolds numbers in ellipsoids, which could be used as simple benchmarks for future dynamo studies in such geometries. We finally discuss how the magnetic boundary conditions can modify the dynamo onset, showing that a perfectly conducting boundary can strongly weaken dynamo action, whereas pseudo-vacuum and insulating boundaries often give similar results.

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J. Vidal and D. Cébron
Thu, 9 Sep 21
49/78

Comments: 20 pages, 10 figures. Published onlined 11 August 2021 in PRSA

Cooling and Instabilities in Colliding Flows [HEAP]

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http://arxiv.org/abs/2109.03282


Collisional self-interactions occurring in protostellar jets give rise to strong shocks, the structure of which can be affected by radiative cooling within the flow. To study such colliding flows, we use the AstroBEAR AMR code to conduct hydrodynamic simulations in both one and three dimensions with a power law cooling function. The characteristic length and time scales for cooling are temperature dependent and thus may vary as shocked gas cools. When the cooling length decreases sufficiently rapidly the system becomes unstable to the radiative shock instability, which produces oscillations in the position of the shock front; these oscillations can be seen in both the one and three dimensional cases. Our simulations show no evidence of the density clumping characteristic of a thermal instability, even when the cooling function meets the expected criteria. In the three-dimensional case, the nonlinear thin shell instability (NTSI) is found to dominate when the cooling length is sufficiently small. When the flows are subjected to the radiative shock instability, oscillations in the size of the cooling region allow NTSI to occur at larger cooling lengths, though larger cooling lengths delay the onset of NTSI by increasing the oscillation period.

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R. Markwick, A. Frank, J. Carroll-Nellenback, et. al.
Thu, 9 Sep 21
65/78

Comments: 12 pages, 21 figures. Accepted for publication in MNRAS

Velocity structure functions in multiphase turbulence: interpreting kinematics of H$α$ filaments in cool core clusters [GA]

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http://arxiv.org/abs/2109.01771


The central regions of cool-core galaxy clusters harbour multiphase gas with temperatures ranging from $10\ \mathrm{K}$–$10^7\ \mathrm{K}$. Feedback from AGN jets prevents the gas from undergoing a catastrophic cooling flow. However, the exact mechanism of this feedback energy input is unknown, mainly due to the lack of velocity measurements of the hot phase gas, which has large thermal velocities. However, recent observations have measured the velocity structure functions ($\mathrm{VSF}$s) of the cooler phases (at $10\ \mathrm{K}$ and $10^4\ \mathrm{K}$) and used them to indirectly estimate the motions of the hot phase. In the first part of this study, we conduct high-resolution ($384^3$–$1536^3$ resolution elements) simulations of homogeneous isotropic subsonic turbulence, without radiative cooling. We analyse the second-order velocity structure functions ($\mathrm{VSF}_2$) in these simulations and study the effects of varying spatial resolution, the introduction of magnetic fields and the effect of line of sight (LOS) projection on the $\mathrm{VSF}_2$. In the second part of the study, we analyse high-resolution ($768^3$ resolution elements) idealised simulations of multiphase turbulence in the intracluster medium (ICM) from Mohapatra et al 2021. We compare $\mathrm{VSF}_2$ for both the hot ($T\sim10^7\ \mathrm{K}$) and cold ($T\sim10^4\ \mathrm{K}$) phases. We also look for the effect of LOS projection. For turbulence without radiative cooling, we observe a steepening in the slopes of the $\mathrm{VSF}_2$ upon projection. In our runs with radiative cooling and multiphase gas, we find that the $\mathrm{VSF}_2$ of the hot and cold phases have similar scaling, but introducing magnetic fields steepens the $\mathrm{VSF}_2$ of the cold phase only. We also find that projection along the LOS steepens the $\mathrm{VSF}_2$ for the hot phase and mostly flattens it for the cold phase.

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R. Mohapatra, M. Jetti, P. Sharma, et. al.
Tue, 7 Sep 21
1/89

Comments: 17 pages, 11 figures, simulation movies at this youtube playlist: this https URL&list=PLuaNgQ1v_KMauk1cTu_ellwe6-pTkABIh. Submitted to MNRAS, comments are welcome. Companion study at arxiv ID 2107.07722

Turbulent transport of radiation in the solar convective zone [SSA]

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http://arxiv.org/abs/2108.12767


A turbulent transport of radiation in the solar convective zone is investigated. The mean-field equation for the irradiation intensity is derived. It is shown that due to the turbulent effects, the effective penetration length of radiation can be increased in several times in comparison with the mean penetration length of radiation (defined as an inverse mean absorption coefficient). Using the model of the solar convective zone based on the mixing length theory, where the mean penetration length of radiation is usually much smaller than the turbulent correlation length, it is demonstrated that the ratio of the effective penetration length to the mean penetration length of radiation increases in 2.5 times in the vicinity of the solar surface. The main reason are the compressibility effects that become important in the vicinity of the solar surface where temperature and density fluctuations increase towards the solar surface, enhancing fluctuations of the radiation absorption coefficient and increasing the effective penetration length of radiation.

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I. Rogachevskii and N. Kleeorin
Tue, 31 Aug 21
14/73

Comments: 10 pages, 7 figures, mn2e class. arXiv admin note: text overlap with arXiv:2008.00964

Helical turbulent nonlinear dynamo at large magnetic Reynolds numbers [CL]

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http://arxiv.org/abs/2108.12037


The excitation and further sustenance of large-scale magnetic fields in rotating astrophysical systems, including planets, stars and galaxies, is generally thought to involve a fluid magnetic dynamo effect driven by helical magnetohydrodynamic turbulence. While this scenario is appealing on general grounds, it however currently remains largely unconstrained, notably because a fundamental understanding of the nonlinear asymptotic behaviour of large-scale fluid magnetism in the astrophysically-relevant but treacherous regime of large magnetic Reynolds number $Rm$ is still lacking. We explore this problem using local high-resolution simulations of turbulent magnetohydrodynamics driven by an inhomogeneous helical forcing generating a sinusoidal profile of kinetic helicity, mimicking the hemispheric distribution of kinetic helicity in rotating turbulent fluid bodies. We identify a transition at large $Rm$ to an asymptotic nonlinear state, followed up to $Rm\simeq 3\times 10^3$, characterized by an asymptotically small resistive dissipation of magnetic helicity, by its efficient spatial redistribution across the equator through turbulent fluxes driven by the hemispheric distribution of kinetic helicity, and by the presence in the tangled dynamical magnetic field of plasmoids typical of reconnection at large $Rm$.

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F. Rincon
Mon, 30 Aug 21
6/38

Comments: 7 pages, 6 figures (some in low-res), submitted

Dynamo and the Adiabatic Invariant [EPA]

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http://arxiv.org/abs/2108.11548


The paper considers dynamo generated by a shallow fluid layer in a celestial body (planet or star). This dynamo is based on the extra invariant for interacting magnetic Rossby waves. The magnetohydrodynamics (MHD) is linearized on the background of strong toroidal magnetic field. The extra invariant is used to show that the background field is maintained.

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A. Balk
Fri, 27 Aug 21
28/67

Comments: 12 pages, 2 figures

Deep learning for surrogate modelling of 2D mantle convection [EPA]

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http://arxiv.org/abs/2108.10105


Traditionally, 1D models based on scaling laws have been used to parameterized convective heat transfer rocks in the interior of terrestrial planets like Earth, Mars, Mercury and Venus to tackle the computational bottleneck of high-fidelity forward runs in 2D or 3D. However, these are limited in the amount of physics they can model (e.g. depth dependent material properties) and predict only mean quantities such as the mean mantle temperature. We recently showed that feedforward neural networks (FNN) trained using a large number of 2D simulations can overcome this limitation and reliably predict the evolution of entire 1D laterally-averaged temperature profile in time for complex models [Agarwal et al. 2020]. We now extend that approach to predict the full 2D temperature field, which contains more information in the form of convection structures such as hot plumes and cold downwellings. Using a dataset of 10,525 two-dimensional simulations of the thermal evolution of the mantle of a Mars-like planet, we show that deep learning techniques can produce reliable parameterized surrogates (i.e. surrogates that predict state variables such as temperature based only on parameters) of the underlying partial differential equations. We first use convolutional autoencoders to compress the temperature fields by a factor of 142 and then use FNN and long-short term memory networks (LSTM) to predict the compressed fields. On average, the FNN predictions are 99.30% and the LSTM predictions are 99.22% accurate with respect to unseen simulations. Proper orthogonal decomposition (POD) of the LSTM and FNN predictions shows that despite a lower mean absolute relative accuracy, LSTMs capture the flow dynamics better than FNNs. When summed, the POD coefficients from FNN predictions and from LSTM predictions amount to 96.51% and 97.66% relative to the coefficients of the original simulations, respectively.

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S. Agarwal, N. Tosi, P. Kessel, et. al.
Tue, 24 Aug 21
66/76

Comments: N/A

Saturation of large-scale dynamo in anisotropically forced turbulence [SSA]

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http://arxiv.org/abs/2108.08740


Turbulent dynamo theories have faced difficulties in obtaining evolution of large-scale magnetic fields on short dynamical time-scales due to the constraint imposed by magnetic helicity balance. This has critical implications for understanding the large-scale magnetic field evolution in astrophysical systems like the Sun, stars and galaxies. Direct numerical simulations (DNS) in the past with isotropically forced helical turbulence have shown that large-scale dynamo saturation time-scales are dependent on the magnetic Reynolds number (Rm). In this work, we have carried out periodic box DNS of helically forced turbulence leading to a large-scale dynamo with two kinds of forcing function, an isotropic one based on that used in PENCIL-CODE and an anisotropic one based on Galloway-Proctor flows. We show that when the turbulence is forced anisotropically, the nonlinear (saturation) behaviour of the large-scale dynamo is only weakly dependent on Rm. In fact the magnetic helicity evolution on small and large scales in the anisotropic case is distinctly different from that in the isotropic case. This result possibly holds promise for the alleviation of important issues like catastrophic quenching.

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P. Bhat
Fri, 20 Aug 21
36/59

Comments: 9 pages, 10 figures, comments welcome

Resonant tidal responses in rotating fluid bodies: global modes hidden beneath localized wave beams [CL]

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http://arxiv.org/abs/2108.08515


In rotating stars and planets, excitation of inertial waves in convective envelopes provides an important channel for tidal dissipation, but the dissipation rate due to inertial waves depends erratically on the tidal frequency. Tidal dissipation is significantly enhanced at some frequencies, suggesting possible resonances between the tidal forcing and some eigenmodes. However, the nature of these resonances remains enigmatic owing to the singularity of the eigenvalue problem of inertial waves, and the resonances are often mistakenly attributed to wave attractors in the literature. In this letter, we reveal that resonant tidal responses correspond to inertial modes with large-scale flows hidden beneath localized wave beams. Strong couplings between the tidal forcing and the hidden large-scale flows intensify the localized wave beams emanating from the critical latitudes, leading to enhanced tidal dissipation. This study resolves a long-standing puzzle regarding the frequency-dependence of tidal dissipation due to inertial waves in convective envelopes.

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Y. Lin and G. Ogilvie
Fri, 20 Aug 21
51/59

Comments: 11 pages, 5 figures, Accepted for publication in ApJL

Librations of a body composed of a deformable mantle and a fluid core [EPA]

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http://arxiv.org/abs/2108.07762


We present fully three-dimensional equations to describe the rotations of a body made of a deformable mantle and a fluid core. The model in its essence is similar to that used by INPOP (Integration Plan\'{e}taire de l’Observatoire de Paris), e.g. Viswanathan et al. (2019), and by JPL (Jet Propulsion Laboratory), e.g. Folkner et al. (2014), to represent the Moon. The intended advantages of our model are: straightforward use of any linear-viscoelastic model for the rheology of the mantle; easy numerical implementation in time-domain (no time lags are necessary); all parameters, including those related to the “permanent deformation”, have a physical interpretation. The paper also contains: 1) A physical model to explain the usual lack of hydrostaticity of the mantle (permanent deformation). 2) Formulas for free librations of bodies in and out-of spin-orbit resonance that are valid for any linear viscoelastic rheology of the mantle. 3) Formulas for the offset between the mantle and the idealized rigid-body motion (Peale’s Cassini states). 4) Applications to the librations of Moon, Earth, and Mercury that are used for model validation.

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C. Ragazzo, G. Boué, Y. Gevorgyan, et. al.
Wed, 18 Aug 21
3/70

Comments: 90 pages, 15 figures

Non-Boussinesq convection at low Prandtl numbers relevant to the Sun [CL]

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http://arxiv.org/abs/2108.04472


Convection in the Sun occurs at Rayleigh numbers, $Ra$, as high as $10^{22}$, molecular Prandtl number, $Pr$, as low as $10^{-6}$, and occurs under conditions that are far from satisfying the Oberbeck-Boussinesq (OB) idealization. The effects of these extreme circumstances on turbulent heat transport are unknown, and no comparable conditions exist on Earth. Our goal is to understand how these effects scale (since we cannot yet replicate the Sun’s conditions faithfully). We study thermal convection by using direct numerical simulations, and determine the variation with respect to $Pr$, up to $Pr$ as low as $10^{-4}$, of the turbulent Prandtl number, $Pr_t$, which is the ratio of turbulent viscosity to thermal diffusivity. The simulations are primarily two-dimensional but we draw upon some three-dimensional results as well. We focus on non-Oberbeck-Boussinesq (NOB) conditions of a certain type, but also study OB convection for comparison. The OB simulations are performed in a rectangular box of aspect ratio 2 by varying $Pr$ from $O(10)$ to $10^{-4}$ at fixed Grashof number $Gr \equiv Ra/Pr = 10^9$. The NOB simulations are done in the same box by letting only the thermal diffusivity depend on the temperature. Here, the Rayleigh number is fixed at the top boundary while the mean $Pr$ varies in the bulk from 0.07 to $5 \times 10^{-4}$. The three-dimensional simulations are performed in a box of aspect ratio 25 at a fixed Rayleigh number of $10^5$, and $0.005 < Pr < 7$. The principal finding is that $Pr_t$ increases with decreasing $Pr$ in both OB and NOB convection: $Pr_t \sim Pr^{-0.3}$ for OB convection and $Pr_t \sim Pr^{-1}$ for the NOB case. The $Pr_t$-dependence for the NOB case especially suggests that convective flows in the astrophysical settings behave effectively as in high-Prandtl-number turbulence.

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A. Pandey, J. Schumacher and K. Sreenivasan
Wed, 11 Aug 21
42/72

Comments: 15 pages, 9 figures, 3 tables

Vortex solution in elliptic coordinates [CL]

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http://arxiv.org/abs/2108.04013


Vortices (flows with closed elliptic streamlines) are exact nonlinear solutions to the compressible Euler equation. In this contribution, we use differential geometry to derive the transformations between Cartesian and elliptic coordinates, and show that in elliptic coordinates a constant vorticity flow reduces to $\dot{\mu}=0$ and $\dot{\nu}={\rm const}$ along the streamline $\mu_0$ that matches the vortex eccentricity.

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W. Lyra
Tue, 10 Aug 21
49/84

Comments: RNAAS Research Notes. & pages, 1 figure

Axisymmetric simulations of the convective overstability in protoplanetary discs [EPA]

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http://arxiv.org/abs/2108.01541


Protoplanetary discs at certain radii exhibit adverse radial entropy gradients that can drive oscillatory convection (`convective overstability’; COS). The ensuing hydrodynamical activity may reshape the radial thermal structure of the disc while mixing solid material radially and vertically or, alternatively, concentrating it in vortical structures. We perform local axisymmetric simulations of the COS using the code SNOOPY, showing first how parasites halt the instability’s exponential growth, and second, the different saturation routes it takes subsequently. As the Reynolds and (pseudo-) Richardson numbers increase, the system moves successively from (a) a weakly nonlinear state characterised by relatively ordered nonlinear waves, to (b) wave turbulence, and finally to (c) the formation of intermittent and then persistent zonal flows. In three-dimensions, we expect the latter flows to spawn vortices in the orbital plane. Given the very high Reynolds numbers in protoplanetary discs, the third regime should be the most prevalent. As a consequence, we argue that the COS is an important dynamical process in planet formation, especially near features such as dead zone edges, ice lines, gaps, and dust rings.

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R. Teed and H. Latter
Wed, 4 Aug 21
17/66

Comments: N/A

Dynamo instabilities in plasmas with inhomogeneous chiral chemical potential [CL]

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http://arxiv.org/abs/2107.13028


We study the dynamics of magnetic fields in chiral magnetohydrodynamics, which takes into account the effects of an additional electric current related to the chiral magnetic effect in high energy plasmas. We perform direct numerical simulations, considering weak seed magnetic fields and inhomogeneities of the chiral chemical potential mu_5 with a zero mean. We demonstrate that a small-scale chiral dynamo can occur in such plasmas if fluctuations of mu_5 are correlated on length scales that are much larger than the scale on which the dynamo growth rate reaches its maximum. Magnetic fluctuations grow by many orders of magnitude due to the small-scale chiral dynamo instability. Once the nonlinear backreaction of the generated magnetic field on fluctuations of mu_5 sets in, the ratio of these scales decreases and the dynamo saturates. When magnetic fluctuations grow sufficiently to drive turbulence via the Lorentz force before saturation occurs, an additional mean-field dynamo phase is identified. The mean magnetic field grows on a scale that is larger than the integral scale of turbulence after the amplification of the fluctuating component saturates. The growth rate of the mean magnetic field is caused by a magnetic alpha effect that is proportional to the current helicity. With the onset of turbulence, the power spectrum of mu_5 develops a universal k^(-1) scaling independently of its initial shape, while the magnetic energy spectrum approaches a k^(-3) scaling.

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J. Schober, I. Rogachevskii and A. Brandenburg
Thu, 29 Jul 21
27/59

Comments: 19 pages, 18 figures

Production of a chiral magnetic anomaly with emerging turbulence and mean-field dynamo action [CL]

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http://arxiv.org/abs/2107.12945


In relativistic magnetized plasmas, asymmetry in the number densities of left- and right-handed fermions, i.e., a non-zero chiral chemical potential mu_5, leads to an electric current along the magnetic field. This causes a chiral dynamo instability for a uniform mu_5, but our simulations reveal dynamos even for fluctuating mu_5 with zero mean. This generates small-scale magnetic helicity and turbulence. A large-scale mu_5 emerges due to chirality conservation. These effects amplify a mean magnetic field via the magnetic alpha effect and produce a universal scale-invariant mu_5 spectrum.

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J. Schober, I. Rogachevskii and A. Brandenburg
Wed, 28 Jul 21
43/68

Comments: 6 pages, 4 figures

Variations of the Martian Thermospheric Gravity Wave Activity during the Recent Solar Minimum as Observed by MAVEN [EPA]

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http://arxiv.org/abs/2107.09875


Atmospheric gravity (buoyancy) waves (GWs) are of great importance for the energy and momentum budget of all planetary atmospheres. Propagating upward waves carry energy and momentum from the lower atmosphere to thermospheric altitudes and re-distribute them there. On Mars, GWs dominate the variability of the thermosphere and ionosphere. We provide a comprehensive climatology of Martian thermospheric GW activity at solar minimum (end of Solar Cycle 24) inferred from measurements by Neutral Gas and Ions Mass Spectrometer on board Mars Atmosphere and Volatile EvolutioN (NGIMS/MAVEN). The results are compared and interpreted using a one-dimensional spectral nonlinear GW model. Monthly mean GW activity varies strongly as a function of altitude (150-230 km) between 6-25%, reaching a maximum at $\sim$170 km. GW activity systematically exhibits a local time variability with nighttime values exceeding those during daytime, in accordance with previous studies. The analysis suggests that the day-night difference is primarily caused by a competition between dissipation due to molecular diffusion and wave growth due to decreasing background density. Thus, convective instability mechanism is likely to play a less important role in limiting GW amplitudes in the upper thermosphere, which explains their local time behavior.

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E. Yiğit, A. Medvedev and P. Hartogh
Thu, 22 Jul 21
26/59

Comments: Accepted in the Astrophysical Journal

Spatio temporal analysis of waves in compressively driven magnetohydrodynamics turbulence [CL]

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http://arxiv.org/abs/2107.09212


Using direct numerical simulations (DNSs), the interaction between linear waves and turbulence under the compressible magnetohydrodynamic (CMHD) approach was studied. A set of DNSs in three dimensions for a spatial resolution of $128^3$ and $256^3$ were performed. A parametric study was carried out varying the sonic Mach number, the mean magnetic field and the compressibility amplitude of the forcing. Spatio-temporal spectra of the magnetic energy were built and analyzed, allowing for direct identification of all wave modes in a CMHD turbulent system and quantification of the amount of energy in each mode as a function of the wave number. Thus, linear waves were detected, that is Alfv\’en waves and fast and slow magnetosonic waves. Furthermore, different responses of the plasma were found according to whether the Mach number or the mean magnetic field was varied. On the other hand, making use of spatio-temporal spectra and two different integration methods, we accurately quantified the amount of energy present in each of the normal modes. Finally, although the presence of linear waves was observed, in all the cases studied the system was mainly dominated by the non-linear dynamics of the plasma.

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M. Brodiano, N. Andrés and P. Dmitruk
Wed, 21 Jul 21
62/83

Comments: arXiv admin note: substantial text overlap with arXiv:1707.09190

The Magnetic Mechanism for Hotspot Reversals in Hot Jupiter Atmospheres [EPA]

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http://arxiv.org/abs/2107.07515


Magnetically-driven hotspot variations (which are tied to atmospheric wind variations) in hot Jupiters are studied using non-linear numerical simulations of a shallow-water magnetohydrodynamic (SWMHD) system and a linear analysis of equatorial SWMHD waves. In hydrodynamic models, mid-to-high latitude geostrophic circulations are known to cause a net west-to-east equatorial thermal energy transfer, which drives hotspot offsets eastward. We find that a strong toroidal magnetic field can obstruct these energy transporting circulations. This results in winds aligning with the magnetic field and generates westward Lorentz force accelerations in hotspot regions, ultimately causing westward hotspot offsets. In the subsequent linear analysis we find that this reversal mechanism has an equatorial wave analogy in terms of the planetary scale equatorial magneto-Rossby waves. We compare our findings to three-dimensional MHD simulations, both quantitively and qualitatively, identifying the link between the mechanics of magnetically-driven hotspot and wind reversals. We use the developed theory to identify physically-motivated reversal criteria, which can be used to place constraints on the magnetic fields of ultra-hot Jupiters with observed westward hotspots.

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A. Hindle, P. Bushby and T. Rogers
Mon, 19 Jul 21
4/70

Comments: 30 pages, 9 figures, 3 tables

Characterising the turbulent multiphase halos with periodic box simulations [GA]

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http://arxiv.org/abs/2107.07722


Turbulence in the intracluster medium (ICM) is driven by active galactic nuclei (AGNs) jets, by mergers, and in the wakes of infalling galaxies. It not only governs gas motion but also plays a key role in the ICM thermodynamics. Turbulence can help seed thermal instability by generating density fluctuations, and mix the hot and cold phases together to produce intermediate temperature gas ($10^4$–$10^7$~$\mathrm{K}$) with short cooling times. We conduct high resolution ($384^3$–$768^3$ resolution elements) idealised simulations of the multiphase ICM and study the effects of turbulence strength, characterised by $f_{\mathrm{turb}}$ ($0.001$–$1.0$), the ratio of turbulent forcing power to the net radiative cooling rate. We analyse density and temperature distribution, amplitude and nature of gas perturbations, and probability of transitions across the temperature phases. We also study the effects of mass and volume-weighted thermal heating and weak ICM magnetic fields. For low $f_{\mathrm{turb}}$, the gas is distribution is bimodal between the hot and cold phases. The mixing between different phases becomes more efficient with increasing $f_{\mathrm{turb}}$, producing larger amounts of the intermediate temperature gas. Strong turbulence ($f_{\mathrm{turb}}\geq0.5$) generates larger density fluctuations and faster cooling, The rms logarithmic pressure fluctuation scaling with Mach number $\sigma_{\ln{\bar{P}}}^2\approx\ln(1+b^2\gamma^2\mathcal{M}^4)$ is unaffected by thermal instability and is the same as in hydro turbulence. In contrast, the density fluctuations characterised by $\sigma_s^2$ are much larger, especially for $\mathcal{M}\lesssim0.5$. In magnetohydrodynamic runs, magnetic fields provide significant pressure support in the cold phase but do not have any strong effects on the diffuse gas distribution, and nature and amplitude of fluctuations.

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R. Mohapatra, M. Jetti, P. Sharma, et. al.
Mon, 19 Jul 21
37/70

Comments: 16 pages, 13 figures, submitted to MNRAS. Simulation movies are in this playlist: this https URL&list=PLuaNgQ1v_KMathKae1SF2nKuJWzL9DQTt

Linear stability of a rotating liquid column revisited [CL]

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http://arxiv.org/abs/2107.06498


We revisit the somewhat classical problem of the linear stability of a rigidly rotating liquid column in this communication. Although literature pertaining to this problem dates back to 1959, the relation between inviscid and viscous stability criteria has not yet been clarified. While the viscous criterion for stability, given by $We = n^2+k^2-1$, is both necessary and sufficient, this relation has only been shown to be sufficient in the inviscid case. Here, $We = \rho \Omega^2 a^3/\gamma$ is the Weber number and measures the relative magnitudes of the centrifugal and surface tension forces, with $\Omega$ being the angular velocity of the rigidly rotating column, $a$ the column radius, $\rho$ the density of the fluid, and $\gamma$ the surface tension coefficient; $k$ and $n$ denote the axial and azimuthal wavenumbers of the imposed perturbation. We show that the subtle difference between the inviscid and viscous criteria arises from the surprisingly complicated picture of inviscid stability in the $We-k$ plane. For all $n >1$, the viscously unstable region, corresponding to $We > n^2+k^2-1$, contains an infinite hierarchy of inviscidly stable islands ending in cusps, with a dominant leading island. Only the dominant island, now infinite in extent along the $We$ axis, persists for $n= 1$. This picture may be understood, based on the underlying eigenspectrum, as arising from the cascade of coalescences between a retrograde mode, that is the continuation of the cograde surface-tension-driven mode across the zero Doppler frequency point, and successive retrograde Coriolis modes constituting an infinite hierarchy.

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P. Dubey, A. Roy and G. Subramanian
Thu, 15 Jul 21
8/63

Comments: 22 pages, 13 figures

Dust in the Wind with Resonant Drag Instabilities: I. The Dynamics of Dust-Driven Outflows in GMCs and HII Regions [GA]

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http://arxiv.org/abs/2107.04608


Radiation-dust driven outflows, where radiation pressure on dust grains accelerates gas, occur in many astrophysical environments. Almost all previous numerical studies of these systems have assumed that the dust was perfectly-coupled to the gas. However, it has recently been shown that the dust in these systems is unstable to a large class of ‘resonant drag instabilities’ (RDIs) which de-couple the dust and gas dynamics and could qualitatively change the nonlinear outcome of these outflows. We present the first simulations of radiation-dust driven outflows in stratified, inhomogeneous media, including explicit grain dynamics and a realistic spectrum of grain sizes and charge, magnetic fields and Lorentz forces on grains (which dramatically enhance the RDIs), Coulomb and Epstein drag forces, and explicit radiation transport allowing for different grain absorption and scattering properties. In this paper we consider conditions resembling giant molecular clouds (GMCs), HII regions, and distributed starbursts, where optical depths are modest ($\lesssim 1$), single-scattering effects dominate radiation-dust coupling, Lorentz forces dominate over drag on grains, and the fastest-growing RDIs are similar, such as magnetosonic and fast-gyro RDIs. These RDIs generically produce strong size-dependent dust clustering, growing nonlinear on timescales that are much shorter than the characteristic times of the outflow. The instabilities produce filamentary and plume-like or ‘horsehead’ nebular morphologies that are remarkably similar to observed dust structures in GMCs and HII regions. Additionally, in some cases they strongly alter the magnetic field structure and topology relative to filaments. Despite driving strong micro-scale dust clumping which leaves some gas ‘behind,’ an order-unity fraction of the gas is always efficiently entrained by dust.

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P. Hopkins, A. Rosen, J. Squire, et. al.
Tue, 13 Jul 21
72/79

Comments: 24 pages, 22 figures, submitted to MNRAS. Comments welcome

Modeling coexisting GSF and shear instabilities in rotating stars [SSA]

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http://arxiv.org/abs/2107.03978


Zahn’s widely-used model for turbulent mixing induced by rotational shear has recently been validated (with some caveats) in non-rotating shear flows. It is not clear, however, whether his model remains valid in the presence of rotation, even though this was its original purpose. Furthermore, new instabilities arise in rotating fluids, such as the Goldreich-Schubert-Fricke (GSF) instability. Which instability dominates when more than one can be excited, and how they influence each other, were open questions that this paper answers. To do so, we use direct numerical simulations of diffusive stratified shear flows in a rotating triply-periodic Cartesian domain located at the equator of a star. We find that either the GSF instability or the shear instability tends to take over the other in controlling the system, suggesting that stellar evolution models only need to have a mixing prescription for each individual instability, together with a criterion to determine which one dominates. However, we also find that it is not always easy to predict which instability “wins” for given input parameters, because the diffusive shear instability is subcritical, and only takes place if there is a finite-amplitude turbulence “primer” to seed it. Interestingly, we find that the GSF instability can in some cases play the role of this primer, thereby providing a pathway to excite the subcritical shear instability. This can also drive relaxation oscillations, that may be observable. We conclude by proposing a new model for mixing in the equatorial regions of stellar radiative zones due to differential rotation.

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E. Chang and P. Garaud
Fri, 9 Jul 21
2/62

Comments: 19 pages, 11 figures

Forced linear shear flows with rotation: rotating Couette-Poiseuille flow, its stability and astrophysical implications [CL]

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http://arxiv.org/abs/2107.04012


We explore the effect of forcing on the linear shear flow or plane Couette flow, which is also the background flow in the very small region of the Keplerian accretion disk. We show that depending on the strength of forcing and boundary conditions suitable for the systems under consideration, the background plane shear flow and, hence, accretion disk velocity profile modifies to parabolic flow, which is plane Poiseuille flow or Couette-Poiseuille flow, depending on the frame of reference. In the presence of rotation, plane Poiseuille flow becomes unstable at a smaller Reynolds number under pure vertical as well as threedimensional perturbations. Hence, while rotation stabilizes plane Couette flow, the same destabilizes plane Poiseuille flow faster and forced local accretion disk. Depending on the various factors, when local linear shear flow becomes Poiseuille flow in the shearing box due to the presence of extra force, the flow becomes unstable even for the Keplerian rotation and hence turbulence will pop in there. This helps in resolving a long standing problem of sub-critical transition to turbulence in hydrodynamic accretion disks and laboratory plane Couette flow.

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S. Ghosh and B. Mukhopadhyay
Fri, 9 Jul 21
58/62

Comments: 21 pages including 28 figures and 1 table; accepted for publication in The Astrophysical Journal (ApJ)

Multidimensional low-Mach number time-implicit hydrodynamic simulations of convective helium shell burning in a massive star [SSA]

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http://arxiv.org/abs/2107.02199


Context. Multidimensional hydrodynamic simulations of convection in stellar interiors are numerically challenging, especially for flows at low Mach numbers.
Methods. We explore the benefits of using a low-Mach hydrodynamic flux solver and demonstrate its usability for simulations in the astrophysical context. The time-implicit Seven-League Hydro (SLH) code was used to perform multidimensional simulations of convective helium shell burning based on a 25 M$\odot$ star model. The results obtained with the low-Mach AUSM$^{+}$-up solver were compared to results when using its non low-Mach variant AUSM$\mathrm{B}^{+}$-up. We applied well-balancing of the gravitational source term to maintain the initial hydrostatic background stratification. The computational grids have resolutions ranging from $180 \times 90^2$ to $810 \times 540^2$ cells and the nuclear energy release was boosted by factors of $3 \times 10^3$, $1 \times 10^4$, and $3 \times 10^4$ to study the dependence of the results on these parameters.
Results. The boosted energy input results in convection at Mach numbers in the range of $10^{-2}$ to $10^{-3}$. Standard mixing-length theory (MLT) predicts convective velocities of about $1.6 \times 10^{-4}$ if no boosting is applied. Simulations with AUSM$^{+}$-up show a Kolmogorov-like inertial range in the kinetic energy spectrum that extends further toward smaller scales compared with its non low-Mach variant. The kinetic energy dissipation of the AUSM$^{+}$-up solver already converges at a lower resolution compared to AUSM$^{+}_{\mathrm{B}}$ -up. The extracted entrainment rates at the boundaries of the convection zone are well represented by the bulk Richardson entrainment law and the corresponding fitting parameters are in agreement with published results for carbon shell burning.

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L. Horst, R. Hirschi, P. Edelmann, et. al.
Wed, 7 Jul 21
17/58

Comments: Accepted for publication in A&A

A covariant approach to relativistic large-eddy simulations: The fibration picture [CL]

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http://arxiv.org/abs/2107.01083


Models of turbulent flows require the resolution of a vast range of scales, from large eddies to small-scale features directly associated with dissipation. As the required resolution is not within reach of large scale numerical simulations, standard strategies involve a smoothing of the fluid dynamics, either through time averaging or spatial filtering. These strategies raise formal issues in general relativity, where the split between space and time is observer dependent. To make progress, we develop a new covariant framework for filtering/averaging based on the fibration of spacetime associated with fluid elements and the use of Fermi coordinates to facilitate a meaningful local analysis. We derive the resolved equations of motion, demonstrating how “effective” dissipative terms arise because of the coarse-graining, and pay particular attention to the thermodynamical interpretation of the resolved quantities. Finally, as the smoothing of the fluid-dynamics inevitably leads to a closure problem, we propose a new closure scheme inspired by recent progress in the modelling of dissipative relativistic fluids, and crucially, demonstrate the linear stability of the proposed model.

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T. Celora, N. Andersson, I. Hawke, et. al.
Mon, 5 Jul 21
14/52

Comments: 24 pages, 1 figure, comments are welcome

An MHD spectral theory approach to Jeans' magnetized gravitational instability [GA]

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http://arxiv.org/abs/2106.07681


In this paper, we revisit the governing equations for linear magnetohydrodynamic (MHD) waves and instabilities existing within a magnetized, plane-parallel, self-gravitating slab. Our approach allows for fully non-uniformly magnetized slabs, which deviate from isothermal conditions, such that the well-known Alfv\’en and slow continuous spectra enter the description. We generalize modern MHD textbook treatments, by showing how self-gravity enters the MHD wave equation, beyond the frequently adopted Cowling approximation. This clarifies how Jeans’ instability generalizes from hydro to magnetohydrodynamic conditions without assuming the usual Jeans’ swindle approach. Our main contribution lies in reformulating the completely general governing wave equations in a number of mathematically equivalent forms, ranging from a coupled Sturm-Liouville formulation, to a Hamiltonian formulation linked to coupled harmonic oscillators, up to a convenient matrix differential form. The latter allows us to derive analytically the eigenfunctions of a magnetized, self-gravitating thin slab. In addition, as an example we give the exact closed form dispersion relations for the hydrodynamical p- and Jeans-unstable modes, with the latter demonstrating how the Cowling approximation modifies due to a proper treatment of self-gravity. The various reformulations of the MHD wave equation open up new avenues for future MHD spectral studies of instabilities as relevant for cosmic filament formation, which can e.g. use modern formal solution strategies tailored to solve coupled Sturm-Liouville or harmonic oscillator problems.

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J. Durrive, R. Keppens and M. Langer
Wed, 16 Jun 21
16/57

Comments: 20 pages, 1 figure, accepted for publication in MNRAS