Tag Archives: Fluid Dynamics

Dynamical analogue spacetimes in non-relativistic flows [CL]

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http://arxiv.org/abs/2106.07618


Analogue gravity models describe linear fluctuations of fluids as a massless scalar field propagating on stationary acoustic spacetimes constructed from the background flow. In this paper, we establish that this paradigm generalizes to arbitrary order nonlinear perturbations propagating on dynamical analogue spacetimes. Our results hold for all inviscid, spherically symmetric and barotropic non-relativistic flows in the presence of an external conservative force. We demonstrate that such fluids always admit a dynamical description governed by a coupled pair of wave and continuity equations. We provide an iterative approach to solve these equations about any known stationary solution to all orders in perturbation. In the process, we reveal that there exists a dynamical acoustic spacetime on which fluctuations of the mass accretion rate propagate. The dynamical acoustic spacetime is shown to have a well defined causal structure and curvature. In addition, we find a classical fluctuation relation for the acoustic horizon of the spacetime that admit scenarios wherein the horizon can grow as well as recede, with the latter being a result with no known analogue in black holes. As an example, we numerically investigate the Bondi flow accreting solution subject to exponentially damped time dependent perturbations. We find that second and higher order classical perturbations possess an acoustic horizon that oscillates and changes to a new stable size at late times. In particular, the case of a receding acoustic horizon is realized through `low frequency’ perturbations. We discuss our results in the context of more general analogue models and its potential implications on astrophysical accretion flows.

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K. Fernandes, S. Maity and T. Das
Tue, 15 Jun 21
32/67

Comments: 42 pages, 33 figures. arXiv admin note: text overlap with arXiv:2005.14114

Conserving Local Magnetic Helicity in Numerical Simulations [CL]

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http://arxiv.org/abs/2106.06078


Magnetic helicity is robustly conserved in systems with large magnetic Reynolds numbers, including most systems of astrophysical interest. This plays a major role in suppressing the kinematic large scale dynamo and driving the large scale dynamo through the magnetic helicity flux. Numerical simulations of astrophysical systems typically lack sufficient resolution to enforce global magnetic helicity over several dynamical times. Errors in the internal distribution of magnetic helicity are equally serious and possibly larger. Here we propose an algorithm for enforcing strict local conservation of magnetic helicity in the Coulomb gauge in numerical simulations.

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Y. Zenati and E. Vishniac
Mon, 14 Jun 21
3/58

Comments: Comments are welcome

Solutions of the imploding shock problem in a medium with varying density [CL]

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http://arxiv.org/abs/2106.04971


We consider the solutions of the Guderley problem, consisting of an imploding strong shock wave in an ideal gas with a power law initial density profile. The self-similar solutions, and specifically the similarity exponent which determines the behavior of the accelerating shock, are studied in detail, for cylindrical and spherical symmetries and for a wide range of the adiabatic index and the spatial density exponent. We then demonstrate how the analytic solutions can be reproduced in Lagrangian hydrodynamic codes, thus demonstrating their usefulness as a code validation and verification test problem.

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I. Giron, S. Balberg and M. Krief
Thu, 10 Jun 21
26/77

Comments: N/A

Role of Surface Gravity Waves in Aquaplanet Ocean Climates [CL]

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http://arxiv.org/abs/2106.05032


We present a set of idealised numerical experiments of a solstitial aquaplanet ocean and examine the thermodynamic and dynamic implications of surface gravity waves (SGWs) upon its mean state. The aquaplanet’s oceanic circulation is dominated by an equatorial zonal jet and four Ekman driven meridional overturning circulation (MOC) cells aligned with the westerly atmospheric jet streams and easterly trade winds in both hemispheres. Including SGW parameterization (representing modulations of air-sea momentum fluxes, Langmuir circulation and Stokes-Coriolis force) increases mixed layer vertical momentum diffusivity by approx. 40% and dampens surface momentum fluxes by approx. 4%. The correspondingly dampened MOC impacts the oceanic density structure to 1 km depth by lessening the large-scale advective transports of heat and salt, freshening the equatorial latitudes (where evaporation minus precipitation [E-P] is negative) and increasing salinity in the subtropics (where E-P is positive) by approx. 1%. The midlatitude pycnocline in both hemispheres is deepened by the inclusion of SGWs. Including SGWs into the aquaplanet ocean model acts to increase mixed layer depth by approx. 10% (up to 20% in the wintertime in midlatitudes), decrease vertical shear in the upper 200 m and alter local midlatitude buoyancy frequency. Generally, the impacts of SGWs upon the aquaplanet ocean are found to be consistent across cooler and warmer climates. We suggest that the implications of these simulations could be relevant to understanding future projections of SGW climate, exoplanetary oceans, and the dynamics of the Southern Ocean mixed layer.

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J. Studholme, M. Markina and S. Gulev
Thu, 10 Jun 21
38/77

Comments: N/A

Scaling of Small-Scale Dynamo Properties in the Rayleigh-Taylor Instability [CL]

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http://arxiv.org/abs/2106.04787


We derive scaling relations based on free-fall and isotropy assumptions for the kinematic small-scale dynamo growth rate and amplification factor over the course of the mixing, saturation, and decay phases of the Rayleigh-Taylor instability (RTI) in a fully-ionized plasma. The scaling relations are tested using sets of three dimensional, visco-resistive MHD simulations of the RTI and found to hold in the saturation phase, but exhibit discrepancies during the mixing and decays phases, suggesting a need to relax either the free-fall or isotropy assumptions. Application of the scaling relations allows for quantitative prediction of the net amplification of magnetic energy in the kinematic dynamo phase and therefore a determination of whether the magnetic energy either remains sub-equipartition at all velocity scales or reaches equipartition with at least some scales of the turbulent kinetic energy in laboratory and astrophysical scenarios. As an example, we consider the dynamo in RTI-unstable regions of the outer envelope of a binary neutron star merger and predict that the kinematic regime of the small-scale dynamo ends on the time scale of nanoseconds and then reaches saturation on a timescale of microseconds, which are both fast compared to the millisecond relaxation time of the post-merger.

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V. Skoutnev, E. Most, A. Bhattacharjee, et. al.
Thu, 10 Jun 21
66/77

Comments: N/A

Optimization of Magnetic Flux Ropes Modeled with the RBSL method [SSA]

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http://arxiv.org/abs/2106.02789


The so-called regularized Biot-Savart laws (RBSLs) provide an efficient and flexible method for modeling pre-eruptive magnetic configurations of coronal mass ejections (CMEs) whose characteristics are constrained by observational images and magnetic-field data. This method allows one to calculate the field of magnetic flux ropes (MFRs) with small circular cross-sections and an arbitrary axis shape. The field of the whole configuration is constructed as a superposition of (1) such a flux-rope field and (2) an ambient potential field derived, for example, from an observed magnetogram. The RBSL kernels are determined from the requirement that the MFR field for a straight cylinder must be exactly force-free. For a curved MFR, however, the magnetic forces are generally unbalanced over the whole path of the MFR. To minimize these forces, we apply a modified Gauss-Newton method to find optimal MFR parameters. This is done by iteratively adjusting the MFR axis path and axial current. We then try to relax the resulting optimized configuration in a subsequent line-tied zero-beta magnetohydrodynamic simulation toward a force-free equilibrium. By considering two models of the sigmoidal pre-eruption configuration for the 2009 February 13 CME, we demonstrate how this approach works and what it is capable of. We show, in particular, that the building blocks of the core magnetic structure described by these models match to morphological features typically observed in such type of configurations. Our method will be useful for both the modeling of particular eruptive events and theoretical studies of idealized pre-eruptive MFR configurations.

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V. Titov, C. Downs, T. Török, et. al.
Tue, 8 Jun 21
86/86

Comments: 21 pages, 11 figures, accepted to ApJS

Diagnosing Turbulence in the Neutral and Molecular Interstellar Medium of Galaxies [GA]

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http://arxiv.org/abs/2106.02239


Magnetohydrodynamic (MHD) turbulence is a crucial component of the current paradigms of star formation, dynamo theory, particle transport, magnetic reconnection and evolution of structure in the interstellar medium (ISM) of galaxies. Despite the importance of turbulence to astrophysical fluids, a full theoretical framework based on solutions to the Navier-Stokes equations remains intractable. Observations provide only limited line-of-sight information on densities, temperatures, velocities and magnetic field strengths and therefore directly measuring turbulence in the ISM is challenging. A statistical approach has been of great utility in allowing comparisons of observations, simulations and analytic predictions. In this review article we address the growing importance of MHD turbulence in many fields of astrophysics and review statistical diagnostics for studying interstellar and interplanetary turbulence. In particular, we will review statistical diagnostics and machine learning algorithms that have been developed for observational data sets in order to obtain information about the turbulence cascade, fluid compressibility (sonic Mach number), and magnetization of fluid (Alfv\’enic Mach number). These techniques have often been tested on numerical simulations of MHD turbulence, which may include the creation of synthetic observations, and are often formulated on theoretical expectations for compressible magnetized turbulence. We stress the use of multiple techniques, as this can provide a more accurate indication of the turbulence parameters of interest. We conclude by describing several open-source tools for the astrophysical community to use when dealing with turbulence.

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B. Burkhart
Mon, 7 Jun 21
17/52

Comments: submitted as a review to Publications of the Astronomical Society of the Pacific; comments welcome

Analytic derivation of the inertial range of compressible turbulence [CL]

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http://arxiv.org/abs/2106.00760


An analytic model for steady state turbulence is employed to obtain the inertial range power spectrum of compressible turbulence. We assume that for homogeneous turbulence, the timescales controlling the energy injected at a given wavenumber from all smaller wave-numbers, are equal for each spatial component. However, the longitudinal component energy is diverted into compression, so the rate controlling the energy that is transferred to all larger wave-numbers by the turbulent viscosity is reduced. The resulting inertial range is a power law with index -2. Indeed such power spectra were observed in various astrophysical settings and also in numerical simulations.

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I. Goldman
Thu, 3 Jun 21
32/55

Comments: 2 pages. Submitted to Phys. Fl

Compressible test-field method and its application to shear dynamos [CL]

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http://arxiv.org/abs/2106.01107


In this study we present a compressible test-field method (CTFM) for computing $\alpha$ effect and turbulent magnetic diffusivity tensors, as well as those relevant for mean ponderomotive force and mass source, applied to the full MHD equations. We describe the theoretical background of the method, and compare it to the quasi-kinematic test-field method (QKTFM), and to the previously studied variant working in simplified MHD (SMHD). We present several test cases using velocity and magnetic fields of the Roberts geometry, and also compare with the imposed-field method. We show that in all cases investigated, the CTFM gives results in agreement with the imposed field method. Some deviations between CTFM and SMHD variant exist. As a relevant physical application, we study non-helically forced shear flows, which exhibit large-scale dynamo (LSD) action, and present a re-analysis of low Reynolds number, moderate shear systems, where we previously neglected the pressure gradient in the momentum equation, and found no coherent shear-current effect. Another key difference is that in the earlier study we used magnetic forcing to mimic small-scale dynamo (SSD) action, while here it is self-consistently driven by purely kinetic forcing. We still find no coherent shear-current effect, but do recover strong large-scale dynamo (LSD) action, that, according to our analysis, is driven through the incoherent effects.

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M. Käpylä, M. Rheinhardt and A. Brandenburg
Thu, 3 Jun 21
44/55

Comments: 16 pages, 10 figures, submitted to the Astrophysical Journal

Thermodynamic stability implies causality [CL]

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http://arxiv.org/abs/2105.14621


The stability conditions of a relativistic hydrodynamic theory can be derived directly from the requirement that the entropy should be maximised in equilibrium. Here we use a simple geometrical argument to prove that, if the hydrodynamic theory is stable according to this entropic criterion, then localised perturbations cannot propagate outside their future light-cone. In other words, within relativistic hydrodynamics, acausal theories must be thermodynamically unstable. We show that the physical origin of this deep connection between stability and causality lies in the relationship between entropy and information.

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L. Gavassino, M. Antonelli and B. Haskell
Tue, 1 Jun 21
63/72

Comments: 9 pages, 2 figures

Convective, absolute and global azimuthal magnetorotational instabilities [CL]

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http://arxiv.org/abs/2105.13470


We study the convective and absolute forms of azimuthal magnetorotational instability (AMRI) in a Taylor-Couette (TC) flow with an imposed azimuthal magnetic field. We show that the domain of the convective AMRI is wider than that of the absolute AMRI. Actually, it is the absolute instability which is the most relevant and important for magnetic TC flow experiments. The absolute AMRI, unlike the convective one, stays in the device, displaying a sustained growth that can be experimentally detected. We also study the global AMRI in a TC flow of finite height using DNS and find that its emerging butterfly-type structure — a spatio-temporal variation in the form of upward and downward traveling waves — is in a very good agreement with the linear stability analysis, which indicates the presence of two dominant absolute AMRI modes in the flow giving rise to this global butterfly pattern.

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A. Mishra, G. Mamatsashvili, V. Galindo, et. al.
Mon, 31 May 21
56/72

Comments: 11 pages, 6 figures, accepted for publication in J. Fluid Mech. Rapids

Nonlinear dynamics of hydrodynamic tori as a model of oscillations and bending waves in astrophysical discs [SSA]

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http://arxiv.org/abs/2105.12465


Understanding oscillations and waves in astrophysical fluid bodies helps to elucidate their observed variability and the underlying physical mechanisms. Indeed, global oscillations and bending modes of accretion discs or tori may be relevant to quasi-periodicity and warped structures around compact objects. While most studies rely on linear theory, observationally significant, nonlinear dynamics is still poorly understood, especially in Keplerian discs for which resonances typically demand a separate treatment. In this work we introduce a novel analytical model which exactly solves the ideal, compressible fluid equations for a non-self-gravitating elliptical cylinder within a local shearing sheet. The aspect ratio of the ring is an adjustable parameter, allowing a continuum of models ranging from a torus of circular cross-section to a thin ring. We restrict attention to flow fields which are a linear function of the coordinates, capturing the lowest order global motions and reducing the dynamics to a set of coupled ordinary differential equations (ODEs). This system acts as a framework for exploring a rich range of hydrodynamic phenomena in both the large amplitude and Keplerian regimes. We demonstrate the connection between tilting tori and warped discs within this model, showing that the linear modes of the ring correspond to oppositely precessing global bending modes. These are further confirmed within a numerical grid based simulation. Crucially, the ODE system developed here allows for a more tractable investigation of nonlinear dynamics. This will be demonstrated in a subsequent paper which evidences mode coupling between warping and vertical motions in thin tilted rings.

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C. Fairbairn and G. Ogilvie
Thu, 27 May 21
21/62

Comments: 14 pages, 7 figures, accepted version for publication in MNRAS

Prandtl number dependence of compressible convection: Flow statistics and convective energy transport [SSA]

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http://arxiv.org/abs/2105.08453


(abridged) Context: The ratio of kinematic viscosity to thermal diffusivity, the Prandtl number, is much smaller than unity in stellar convection zones. Aims: To study the statistics of convective flows and energy transport as functions of the Prandtl number. Methods: Three-dimensional numerical simulations convection in Cartesian geometry are used. The convection zone (CZ) is embedded between two stably stratified layers. Statistics and transport properties of up- and downflows are studied separately. Results: The rms velocity increases with decreasing Prandtl number. At the same time the filling factor of downflows decreases and leads to stronger downflows at lower Prandtl numbers, and to a strong dependence of overshooting on the Prandtl number. Velocity power spectra do not show marked changes as a function of Prandtl number. At the highest Reynolds numbers the velocity power spectra are compatible with the Bolgiano-Obukhov $k^{-11/5}$ scaling. The horizontally averaged convected energy flux ($\overline{F}_{\rm conv}$) is independent of the Prandtl number within the CZ. However, the upflows (downflows) are the dominant contribution to the convected flux at low (high) Prandtl number. These results are similar to those from Rayleigh-Ben\’ard convection in the low Prandtl number regime where convection is vigorously turbulent but inefficient at transporting energy. Conclusions: The current results indicate a strong dependence of convective overshooting and energy flux on the Prandtl number. Numerical simulations of astrophysical convection often use Prandtl number of unity. The current results suggest that this can lead to misleading results and that the astrophysically relevant low Prandtl number regime is qualitatively different from the parameters regimes explored in typical simulations.

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P. Käpylä
Wed, 19 May 21
35/64

Comments: 15 pages, 20 figures, submitted to Astron. Astrophys

Investigating global convective dynamos with mean-field models: full spectrum of turbulent effects required [SSA]

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http://arxiv.org/abs/2105.07708


Turbulent effects are argued to be essential for dynamos in the Sun and stars. While inaccessible observationally, they can be directly studied using global convective dynamo (GCD) simulations. We measure these turbulent effects, in terms of turbulent transport coefficients, from an exemplary GCD simulation using the test-field method. These coefficients are then used as an input into a mean-field (MF) model. We find a good agreement between the MF and GCD solutions, which validates our theoretical approach. This agreement requires all turbulent effects to be included, even those which have been regarded unimportant so far. Our results suggest that simple dynamo models as are commonly used in the solar and stellar community, relying on very few, precisely fine-tuned turbulent effects, may not be representative of the full dynamics of GCDs in astronomical objects.

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J. Warnecke, M. Rheinhardt, M. Viviani, et. al.
Tue, 18 May 21
50/77

Comments: 6 pages with 3 figures, plus 3 pages and 2 figures in the appendix, submitted to ApJ Letters

Surface Manifestation of Stochastically Excited Internal Gravity Waves [SSA]

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http://arxiv.org/abs/2105.04558


Recent photometric observations of massive stars show ubiquitous low-frequency “red-noise” variability, which has been interpreted as internal gravity waves (IGWs). Simulations of IGWs generated by convection show smooth surface wave spectra, qualitatively matching the observed red-noise. On the other hand, theoretical calculations by Shiode et al (2013) and Lecoanet et al (2019) predict IGWs should manifest at the surface as regularly-spaced peaks associated with standing g-modes. In this work, we compare these theoretical approaches to simplified 2D numerical simulations. The simulations show g-mode peaks at their surface, and are in good agreement with Lecoanet et al (2019). The amplitude estimates of Shiode et al (2013) did not take into account the finite width of the g-mode peaks; after correcting for this finite width, we find good agreement with simulations. However, simulations need to be run for hundreds of convection turnover times for the peaks to become visible; this is a long time to run a simulation, but a short time in the life of a star. The final spectrum can be predicted by calculating the wave energy flux spectrum in much shorter simulations, and then either applying the theory of Shiode et al (2013) or Lecoanet et al (2019).

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D. Lecoanet, M. Cantiello, E. Anders, et. al.
Wed, 12 May 21
47/67

Comments: submitted to MNRAS

Spectral characterisation of inertial particle clustering in turbulence [CL]

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http://arxiv.org/abs/2105.01539


Clustering of inertial particles is important for many types of astrophysical and geophysical turbulence, but it has been studied predominately for incompressible flows. Here we study compressible flows and compare clustering in both compressively (irrotationally) and vortically (solenoidally) forced turbulence. Vortically and compressively forced flows are driven stochastically either by solenoidal waves or by circular expansion waves, respectively. For compressively forced flows, the power spectra of the density of inertial particles are a particularly sensitive tool for displaying particle clustering relative to the density enhancement. We use both Lagrangian and Eulerian descriptions for the particles. Particle clustering through shock interaction is found to be particularly prominent in turbulence driven by spherical expansion waves. It manifests itself through a double-peaked distribution of spectral power as a function of Stokes number. The two peaks are associated with two distinct clustering mechanisms; shock interaction for smaller Stokes numbers and the centrifugal sling effect for larger values. The clustering of inertial particles is associated with the formation of caustics. Such caustics can only be captured in the Lagrangian description, which allows us to assess the relative importance of caustics in vortically and irrotationally forced turbulence. We show that the statistical noise resulting from the limited number of particles in the Lagrangian description can be removed from the particle power spectra, allowing us a more detailed comparison of the residual spectra. We focus on the Epstein drag law relevant for rarefied gases, but show that our findings apply also to the usual Stokes drag.

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N. Haugen, A. Brandenburg, C. Sandin, et. al.
Thu, 6 May 21
16/55

Comments: 28 pages, 22 figures, 5 tables, submitted to JFM

Magnetorotational instability with smoothed particle hydrodynamics [SSA]

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http://arxiv.org/abs/2105.01091


We present a thorough numerical study on the MRI using the smoothed particle magnetohydrodynamics method (SPMHD) with the geometric density average force expression (GDSPH). We perform shearing box simulations with different initial setups and a wide range of resolution and dissipation parameters. We show, for the first time, that MRI with sustained turbulence can be simulated successfully with SPH, with results consistent with prior work with grid-based codes. In particular, for the stratified boxes, our simulations reproduce the characteristic butterfly diagram of the MRI dynamo with saturated turbulence for at least 100 orbits. On the contrary, traditional SPH simulations suffer from runaway growth and develop unphysically large azimuthal fields, similar to the results from a recent study with mesh-less methods. We investigated the dependency of MRI turbulence on the numerical Prandtl number in SPH, focusing on the unstratified, zero net-flux case. We found that turbulence can only be sustained with a Prandtl number larger than $\sim$2.5, similar to the critical values of physical Prandtl number found in grid-code simulations. However, unlike grid-based codes, the numerical Prandtl number in SPH increases with resolution, and for a fixed Prandtl number, the resulting magnetic energy and stresses are independent of resolution. Mean-field analyses were performed on all simulations, and the resulting transport coefficients indicate no $\alpha$-effect in the unstratified cases, but an active $\alpha\Omega$ dynamo and a diamagnetic pumping effect in the stratified medium, which are generally in agreement with previous studies. There is no clear indication of a shear-current dynamo in our simulation, which is likely to be responsible for a weaker mean-field growth in the tall, unstratified, zero net-flux simulation.

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R. Wissing, S. Shen, J. Wadsley, et. al.
Wed, 5 May 21
31/61

Comments: N/A

On the interaction between fast tides and convection [SSA]

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http://arxiv.org/abs/2105.00757


The interaction between equilibrium tides and convection in stellar envelopes is often considered important for tidal evolution in close binary and extrasolar planetary systems. Its efficiency for fast tides has however long been controversial, when the tidal frequency exceeds the turnover frequency of convective eddies. Recent numerical simulations indicate that convection can act like an effective viscosity which decays quadratically with tidal frequency for fast tides, resulting in inefficient dissipation in many applications involving pre- and main-sequence stars and giant planets. A new idea was however recently proposed by Terquem (2021), who suggested Reynolds stresses involving correlations between tidal flow components dominate the interaction instead of correlations between convective flow components as usually assumed. They further showed that this can potentially significantly enhance tidal dissipation for fast tides in many applications. Motivated by the importance of this problem for tidal dissipation in stars and planets, we directly compute this new term using analytical arguments and global spherical simulations using Boussinesq and anelastic hydrodynamic models. We demonstrate that the new term proposed by Terquem vanishes identically for equilibrium tides interacting with convection in both Boussinesq and anelastic models; it is therefore unlikely to contribute to tidal dissipation in stars and planets.

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A. Barker and A. Astoul
Tue, 4 May 21
65/72

Comments: 5 pages, 1 figure, submitted to MNRAS Letters. Comments welcome!

Large dust fractions can prevent the propagation of soundwaves [SSA]

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http://arxiv.org/abs/2104.13787


Dust plays a central role in several astrophysical processes. Hence the need of dust/gas numerical solutions, and analytical problems to benchmark them. In the seminal dustywave problem, we discover a regime where sound waves can not propagate through the mixture above a large critical dust fraction. We characterise this regime analytically, making it of use for testing accuracy of numerical solvers at large dust fractions.

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T. David–Cléris and G. Laibe
Thu, 29 Apr 21
48/50

Comments: Accepted for publication in MNRAS

On the shear-current effect: toward understanding why theories and simulations have mutually and separately conflicted [CL]

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http://arxiv.org/abs/2104.11112


The shear-current effect (SCE) of mean-field dynamo theory refers to the combination of a shear flow and a turbulent coefficient $\beta_{21}$ with a favorable negative sign for exponential mean-field growth, rather than positive for diffusion. There have been long standing disagreements among theoretical calculations and comparisons of theory with numerical experiments as to the sign of kinetic ($\beta^u_{21}$) and magnetic ($\beta^b_{21}$) contributions. To resolve these discrepancies, we combine an analytical approach with simulations, and show that unlike $\beta^b_{21}$, the kinetic SCE $\beta^u_{21}$ has a strong dependence on the kinetic energy spectral index and can transit from positive to negative values at $\mathcal{O}(10)$ Reynolds numbers if the spectrum is not too steep. Conversely, $\beta^b_{21}$ is always negative regardless of the spectral index and Reynolds numbers. For very steep energy spectra, the positive $\beta^u_{21}$ can dominate even at energy equipartition $u_\text{rms}\simeq b_\text{rms}$, resulting in a positive total $\beta_{21}$ even though $\beta^b_{21}<0$. Our findings bridge the gap between the seemingly contradictory results from the second-order-correlation approximation (SOCA) versus the spectral-$\tau$ closure (STC), for which opposite signs for $\beta^u_{21}$ have been reported, with the same sign for $\beta^b_{21}<0$. The results also offer an explanation for the simulations that find $\beta^u_{21}>0$ and an inconclusive overall sign of $\beta_{21}$ for $\mathcal{O}(10)$ Reynolds numbers. The transient behavior of $\beta^u_{21}$ is demonstrated using the kinematic test-field method. We compute dynamo growth rates for cases with or without rotation, and discuss opportunities for further work.

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H. Zhou and E. Blackman
Fri, 23 Apr 2021
31/48

Comments: 17 pages, 12 figures; submitted to MNRAS

The traditional approximation of rotation for rapidly rotating stars and planets. I. The impact of strong deformation [SSA]

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http://arxiv.org/abs/2104.09302


The Traditional Approximation of Rotation (TAR) is a treatment of the hydrodynamic equations of rotating and stably stratified fluids in which the action of the Coriolis acceleration along the direction of the entropy and chemical stratifications is neglected because it is weak in comparison with the buoyancy force. The dependent variables in the equations for the dynamics of gravito-inertial waves (GIWs) then become separable into radial and horizontal parts as in the non-rotating case. The TAR is built on the assumptions that the star is spherical (i.e. its centrifugal deformation is neglected) and uniformly rotating. We study the feasibility of carrying out a generalisation of the TAR to account for the centrifugal acceleration in the case of strongly deformed uniformly and rapidly rotating stars (and planets), and to identify the validity domain of this approximation. We built analytically a complete formalism that allows the study of the dynamics of GIWs in spheroidal coordinates which take into account the flattening of rapidly rotating stars by assuming the hierarchies of frequencies adopted within the TAR in the spherical case and by deriving a generalised Laplace tidal equation for the horizontal eigenfunctions of the GIWs and their asymptotic wave periods, which can be used to probe the structure and dynamics of rotating deformed stars with asteroseismology. Using 2D ESTER stellar models, we determine the validity domain of the generalised TAR as a function of the rotation rate of the star normalised by its critical angular velocity and its pseudo-radius. This generalisation allows us to study the signature of the centrifugal effects on GIWs in rapidly rotating deformed stars. We found that the effects of the centrifugal acceleration in rapidly rotating early-type stars on GIWs are theoretically detectable in modern space photometry using observations from Kepler.

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H. Dhouib, V. Prat, T. Reeth, et. al.
Tue, 20 Apr 2021
9/72

Comments: 17 pages, 14 figures, 1 table, abstract shortened for arXiv. Submitted to A&A

Applying the Gibbs stability criterion to relativistic hydrodynamics [CL]

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http://arxiv.org/abs/2104.09142


The stability of the equilibrium state is one of the crucial tests a hydrodynamic theory needs to pass. A widespread technique to study this property consists of searching for a Lyapunov function of the linearised theory, in the form of a quadratic energy-like functional. For relativistic fluids, the explicit expression of such a functional is often found by guessing and lacks a clear physical interpretation. We present a quick, rigorous and systematic technique for constructing the functional of a generic relativistic fluid theory, based on the maximum entropy principle. The method gives the expected result in those cases in which the functional was already known. For the method to be applicable, there must be an entropy current with non-negative four-divergence. This result is an important step towards a definitive resolution of the major open problems connected with relativistic dissipation.

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L. Gavassino
Tue, 20 Apr 2021
52/72

Comments: 13 pages, 1 captioned figure

Analytic solutions of the nonlinear radiation diffusion equation with an instantaneous point source in non-homogeneous media [CL]

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http://arxiv.org/abs/2104.08475


Analytic solutions to the nonlinear radiation diffusion equation with an instantaneous point source for a non-homogeneous medium with a power law spatial density profile, are presented. The solutions are a generalization of the well known solutions for a homogeneous medium. It is shown that the solutions take various qualitatively different forms according to the value of the spatial exponent. These different forms are studied in detail for linear and non linear heat conduction. In addition, by inspecting the generalized solutions, we show that there exist values of the spatial exponent such the conduction front has constant speed or even accelerates. Finally, the various solution forms are compared in detail to numerical simulations, and a good agreement is achieved.

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M. Krief
Tue, 20 Apr 2021
62/72

Comments: The following article has been accepted for publication in Physics of Fluids

Mixing matters [GA]

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http://arxiv.org/abs/2104.07673


All hydrodynamical simulations of turbulent astrophysical phenomena require sub-grid scale models to properly treat energy dissipation and metal mixing. We present the first implementation and application of an anisotropic eddy viscosity and metal mixing model in Lagrangian astrophysical simulations, including a dynamic procedure for the model parameter. We compare these two models directly to the common Smagorinsky and dynamic variant. Using the mesh-free finite mass method as an example, we show that the anisotropic model is best able to reproduce the proper Kolmogorov inertial range scaling in homogeneous, isotropic turbulence. Additionally, we provide a method to calibrate the metal mixing rate that ensures numerical convergence. In our first application to cosmological simulations, we find that all models strongly impact the early evolution of galaxies leading to differences in enrichment and thermodynamic histories. The anisotropic model has the strongest impact, with little difference between the dynamic and the constant-coefficient variant. We also find that the metal distribution functions in the circumgalactic gas are significantly tighter at all redshifts, with the anisotropic model providing the tightest distributions. This is contrary to a recent study that found metal mixing to be relatively unimportant on cosmological scales. In all of our experiments the constant-coefficient Smagorinsky and anisotropic models rivaled their dynamic counterparts, suggesting that the computationally inexpensive constant-coefficient models are viable alternatives in cosmological contexts.

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D. Rennehan
Mon, 19 Apr 2021
2/74

Comments: 18 pages, 7 figures, comments welcome! submitted to MNRAS

ISRU Implications for Lunar and Martian Plume Effects [EPA]

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http://arxiv.org/abs/2104.06248


Experiments, analyses, and simulations have shown that the engine exhaust plume of a Mars lander large enough for human spaceflight will create a deep crater in the martian soil, blowing ejecta to approximately 1 km distance, damaging the bottom of the lander with high-momentum rock impacts, and possibly tilting the lander as the excavated hole collapses to become a broad residual crater upon engine cutoff. Because of this, we deem that we will not have adequate safety margins to land humans on Mars unless we robotically stabilize the soil to form in situ landing pads prior to the mission. It will take a significant amount of time working in a harsh off-planet environment to develop and certify the new technologies and procedures for in situ landing pad construction. The only place to reasonably accomplish this is on the Moon.

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P. Metzger, X. Li, C. Immer, et. al.
Wed, 14 Apr 2021
63/67

Comments: 19 pages, 17 figures

Modification of Roberts' Theory for Rocket Exhaust Plumes Eroding Lunar Soil [EPA]

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http://arxiv.org/abs/2104.05198


Roberts’ model of lunar soil erosion beneath a landing rocket has been updated in several ways to predict the effects of future lunar landings. The model predicts, among other things, the number of divots that would result on surrounding hardware due to the impact of high velocity particulates, the amount and depth of surface material removed, the volume of ejected soil, its velocity, and the distance the particles travel on the Moon. The results are compared against measured results from the Apollo program and predictions are made for mitigating the spray around a future lunar outpost.

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P. Metzger, J. Lane and C. Immer
Tue, 13 Apr 2021
46/93

Comments: 8 pages, 8 figures

Craters Formed in Granular Beds by Impinging Jets of Gas [CL]

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http://arxiv.org/abs/0905.4851


When a jet of gas impinges vertically on a granular bed and forms a crater, the grains may be moved by several different mechanisms: viscous erosion, diffused gas eruption, bearing capacity failure, and/or diffusion-driven shearing. The relative importance of these mechanisms depends upon the flow regime of the gas, the mechanical state of the granular material, and other physical parameters. Here we report research in two specific regimes: viscous erosion forming scour holes as a function of particle size and gravity; and bearing capacity failure forming deep transient craters as a function of soil compaction.

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P. Metzger, R. III, J. Schuler, et. al.
Tue, 13 Apr 2021
48/93

Comments: 4 pages; Powders and Grains 2009, Golden, Colorado, USA

Jet-induced cratering of a granular surface with application to lunar spaceports [CL]

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http://arxiv.org/abs/0906.0196


The erosion of lunar soil by rocket exhaust plumes is investigated experimentally. This has identified the diffusion-driven flow in the bulk of the sand as an important but previously unrecognized mechanism for erosion dynamics. It has also shown that slow regime cratering is governed by the recirculation of sand in the widening geometry of the crater. Scaling relationships and erosion mechanisms have been characterized in detail for the slow regime. The diffusion-driven flow occurs in both slow and fast regime cratering. Because diffusion-driven flow had been omitted from the lunar erosion theory and from the pressure cratering theory of the Apollo and Viking era, those theories cannot be entirely correct.

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P. Metzger, C. Immer, C. Donahue, et. al.
Tue, 13 Apr 2021
50/93

Comments: 13 pages, link to published version: this http URL

Empirical Scaling Laws of Rocket Exhaust Cratering [EPA]

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http://arxiv.org/abs/2104.05176


When launching or landing a spacecraft on the regolith of a terrestrial surface, special attention needs to be paid to the rocket exhaust cratering effects. If the effects are not controlled, the rocket cratering could damage the spacecraft or other surrounding hardware. The cratering effects of a rocket landing a planet’s surface are not understood well, especially for the lunar case with the plume expanding in vacuum. As a result, the blast effects cannot be estimated sufficiently using analytical theories. It is necessary to develop physics-based simulation tools in order to calculate mission-essential parameters. In this work we test out the scaling laws of the physics in regard to growth rate of the crater depth. This will provide the physical insight necessary to begin the physics-based modeling.

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C. Donohue, P. Metzger and C. Immer
Tue, 13 Apr 2021
53/93

Comments: 3 pages, 3 figures

Cratering of Soil by Impinging Jets of Gas, with Application to Landing Rockets on Planetary Surfaces [EPA]

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http://arxiv.org/abs/2104.05195


Several physical mechanisms are involved in excavating granular materials beneath a vertical jet of gas. These occur, for example, beneath the exhaust plume of a rocket landing on the soil of the Moon or Mars. A series of experiments and simulations have been performed to provide a detailed view of the complex gas/soil interactions. Measurements have also been taken from the Apollo lunar landing videos and from photographs of the resulting terrain, and these help to demonstrate how the interactions extrapolate into the lunar environment. It is important to understand these processes at a fundamental level to support the on-going design of higher-fidelity numerical simulations and larger-scale experiments. These are needed to enable future lunar exploration wherein multiple hardware assets will be placed on the Moon within short distances of one another. The high-velocity spray of soil from landing spacecraft must be accurately predicted and controlled lest it erosively damage the surrounding hardware.

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P. Metzger, B. Vu, D. Taylor, et. al.
Tue, 13 Apr 2021
54/93

Comments: 6 pages, 5 figures

The Solar Cycle Variations of the Anisotropy of Taylor Scale and Correlation Scale in the Solar Wind Turbulence [CL]

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http://arxiv.org/abs/2104.04920


The field-aligned anisotropy of the solar wind turbulence, which is quantified by the ratio of the parallel to the perpendicular correlation (and Taylor) length scales, is determined by simultaneous two-point correlation measurements during the time period 2001-2017. Our results show that the correlation scale along the magnetic field is the largest, and the correlation scale in the field-perpendicular directions is the smallest, at both solar maximum and solar minimum. However, the Taylor scale reveals inconsistent results for different stages of the solar cycles. During the years 2001-2004, the Taylor scales are slightly larger in the field-parallel directions, while during the years 2004-2017, the Taylor scales are larger in the field-perpendicular directions. The correlation coefficient between the sunspot number and the anisotropy ratio is employed to describe the effects of solar activity on the anisotropy of solar wind turbulence. The results show that the correlation coefficient regarding the Taylor scale anisotropy (0.65) is larger than that regarding the correlation scale anisotropy (0.43), which indicates that the Taylor scale anisotropy is more sensitive to the solar activity. The Taylor scale and the correlation scale are used to calculate the effective magnetic Reynolds number, which is found to be systematically larger in the field-parallel directions than in the field-perpendicular directions. The correlation coefficient between the sunspot number and the magnetic Reynolds number anisotropy ratio is -0.75. Our results will be meaningful for understanding the solar wind turbulence anisotropy and its long-term variability in the context of solar activity.

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G. Zhou and H. He
Tue, 13 Apr 2021
69/93

Comments: Published in ApJL

Spatio-temporal linear instability analysis for arbitrary dispersion relations on the Lefschetz thimble in multidimensional spacetime [CL]

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http://arxiv.org/abs/1912.11177


In linear stability analysis of field quantities described by partial differential equations, the well-established classical theory is all but impossible to apply to concrete problems in its entirety even for uniform backgrounds when the spatial dimension is more than 1. In this study, using the Lefschetz thimble method, we develop a new formalism to give an explicit expression to the asymptotic behavior of linear perturbations. It is not only more mathematically rigorous than the previous theory but also useful practically in its applications to realistic problems, and, as such, has an impact on broad subjects in physics.

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T. Morinaga and S. Yamada
Wed, 31 Mar 2021
62/62

Comments: 10 pages, 18 figures, accepted for publication in Physical Review Research

Double-diffusive processes in stellar astrophysics [SSA]

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http://arxiv.org/abs/2103.08072


The past 20 years have witnessed a renewal of interest in the subject of double-diffusive processes in astrophysics, and their impact on stellar evolution. This lecture aims to summarize the state of the field as of early 2019, although the reader should bear in mind that it is rapidly evolving. An Annual Review of Fluid Mechanics article entitled “Double-diffusive convection at low Prandtl number” (Garaud, 2018) contains a reasonably comprehensive review of the topic, up to the summer of 2017. I focus here on presenting what I hope are clear derivations of some of the most important results with an astrophysical audience in mind, and discuss their implications for stellar evolution, both in an observational context, and in relation to previous work on the subject.

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P. Garaud
Tue, 16 Mar 21
51/92

Comments: Proceedings of the summer school “Multi-Dimensional Processes In Stellar Physics”. Edited by Michel Rieutord, Isabelle Baraffe and Yveline Lebreton

Revisiting the structure function of PSR B0950+08 scintillations [GA]

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http://arxiv.org/abs/2103.06811


The observational structure function of the scintillations of the radio pulsar PSR B0950+08, was fitted, a decade ago, with a power law with index $1 \pm 0.01$. This was interpreted as an {\em appreciable deviation} from the, commonly observed index of $5/3$, expected for Kolmogorov turbulence. In this paper it is suggested that the observations are consistent with a Kolmogorov turbulence and that the {\em apparent} deviation is due to a turbulent region with an effective depth which is {\em comparable} to the observed lateral scales on the plane of the sky, spanned by the pulsar beam. Alternatively, the fitted index of $1$ is consistent with an underlying compressive turbulence and an even {\it smaller} depth. In the first interpretation the depth is $(5.5 \pm 1.8) \times 10^8 cm$. In the second one, the depth is $\lesssim 4\times 10^7 cm $. These estimates lend support for the existence of extremely thin, ionized scattering screens in the local interstellar cloud, that have been proposed a decade ago.

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I. Goldman
Fri, 12 Mar 21
9/59

Comments: 4 pages, 3 figures, under review in MNRAS

Can we observe the QCD phase transition-generated gravitational waves through pulsar timing arrays? [CEA]

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http://arxiv.org/abs/2102.12428


We perform numerical simulations of gravitational waves (GWs) induced by hydrodynamic and hydromagnetic turbulent sources that might have been present at cosmological quantum chromodynamic (QCD) phase transitions. For turbulent energies of about 4% of the radiation energy density, the typical scale of such motions may have been a sizable fraction of the Hubble scale at that time. The resulting GWs are found to have an energy fraction of about $10^{-9}$ of the critical energy density in the nHz range today and may already have been observed by the NANOGrav collaboration. This is further made possible by our findings of shallower spectra proportional to the square root of the frequency for nonhelical hydromagnetic turbulence. This implies more power at low frequencies than for the steeper spectra previously anticipated. The behavior toward higher frequencies depends strongly on the nature of the turbulence. For vortical hydrodynamic and hydromagnetic turbulence, there is a sharp drop of spectral GW energy by up to five orders of magnitude in the presence of helicity, and somewhat less in the absence of helicity. For acoustic hydrodynamic turbulence, the sharp drop is replaced by a power law decay, albeit with a rather steep slope. Our study supports earlier findings of a quadratic scaling of the GW energy with the magnetic energy of the turbulence and inverse quadratic scaling with the peak frequency, which leads to larger GW energies under QCD conditions.

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A. Brandenburg, E. Clarke, Y. He, et. al.
Thu, 25 Feb 21
7/50

Comments: 13 pages, 8 figures, 3 tables

Enhancement of wave transmissions in multiple radiative and convective zones [CL]

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http://arxiv.org/abs/2102.12018


In this paper, we study wave transmission in a rotating fluid with multiple alternating convectively stable and unstable layers. We have discussed wave transmissions in two different circumstances: cases where the wave is propagative in each layer and cases where wave tunneling occurs. We find that efficient wave transmission can be achieved by resonant propagation' orresonant tunneling’, even when stable layers are strongly stratified, and we call this phenomenon `enhanced wave transmission’. Enhanced wave transmission only occurs when the total number of layers is odd (embedding stable layers are alternatingly embedded within clamping convective layers, or vise versa). For wave propagation, the occurrence of enhanced wave transmission requires that clamping layers have similar properties, the thickness of each clamping layer is close to a multiple of the half wavelength of the corresponding propagative wave, and the total thickness of embedded layers is close to a multiple of the half wavelength of the corresponding propagating wave (resonant propagation). For wave tunneling, we have considered two cases: tunneling of gravity waves and tunneling of inertial waves. In both cases, efficient tunneling requires that clamping layers have similar properties, the thickness of each embedded layer is much smaller than the corresponding e-folding decay distance, and the thickness of each clamping layer is close to a multiple-and-a-half of half wavelength (resonant tunneling).

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T. Cai, C. Yu and X. Wei
Thu, 25 Feb 21
44/50

Comments: accepted to J. Fluid Mech

Revisiting the Strong Shock Problem: Converging and Diverging Shocks in Different Geometries [HEAP]

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http://arxiv.org/abs/2102.07235


Self-similar solutions to converging (implosions) and diverging (explosions) shocks have been studied before, in planar, cylindrical or spherical symmetry. Here we offer a unified treatment of these apparently disconnected problems . We study the flow of an ideal gas with adiabatic index $\gamma$ with initial density $\rho\sim r^{-\omega}$, containing a strong shock wave. We characterize the self-similar solutions in the entirety of the parameter space $\gamma,\omega$, and draw the connections between the different geometries. We find that the so-called “gap” in diverging shocks does not exist in planar geometry, and that only type II self-similar solutions are valid in converging shocks. We also find that in some cases, a converging shock might not create a reflected shock after its convergence. Finally, we derive analytical approximations for the similarity exponent in the entirety of parameter space.

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E. Modelevsky and R. Sari
Tue, 16 Feb 21
20/63

Comments: 12 pages, 11 figures

A multi-shock model for the density variance of anisotropic, highly-magnetised, supersonic turbulence [GA]

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http://arxiv.org/abs/2102.00629


Shocks form the basis of our understanding for the density and velocity statistics of supersonic turbulent flows, such as those found in the cool interstellar medium (ISM). The variance of the density field, $\sigma^2_{\rho/\rho_0}$, is of particular interest for molecular clouds (MCs), the birthplaces of stars in the Universe. The density variance may be used to infer underlying physical processes in an MC, and parameterises the star formation (SF) rate of a cloud. However, models for $\sigma^2_{\rho/\rho_0}$ all share a common feature — the variance is assumed to be isotropic. This assumption does not hold when a trans/sub-Alfv\’enic mean magnetic field, $\vec{B}0$, is present in the cloud, which observations suggest is relevant for some MCs. We develop an anisotropic model for $\sigma{\rho/\rho_0}^2$, using contributions from hydrodynamical and fast magnetosonic shocks that propagate orthogonal to each other. Our model predicts an upper bound for $\sigma_{\rho/\rho_0}^2$ in the high Mach number $(\mathcal{M})$ limit as small-scale density fluctuations become suppressed by the strong $\vec{B}0$. The model reduces to the isotropic $\sigma{\rho/\rho_0}^2-\mathcal{M}$ relation in the hydrodynamical limit. To validate our model, we calculate $\sigma_{\rho/\rho_0}^2$ from 12~high-resolution, three-dimensional, supersonic, sub-Alfv\’enic magnetohydrodynamical (MHD) turbulence simulations and find good agreement with our theory. We discuss how the two MHD shocks may be the bimodally oriented over-densities observed in some MCs and the implications for SF theory in the presence of a sub-Alfv\’enic $\vec{B}_0$. By creating an anisotropic, supersonic density fluctuation model, this study paves the way for SF theory in the highly anisotropic regime of interstellar turbulence.

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J. Beattie, P. Mocz, C. Federrath, et. al.
Tue, 2 Feb 21
50/86

Comments: 16 pages, 7 figures, submitted to MNRAS

Efficient highly-subsonic turbulent dynamo and growth of primordial magnetic fields [HEAP]

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http://arxiv.org/abs/2101.08256


We present the first study on the amplification of magnetic fields by the turbulent dynamo in the highly subsonic regime, with Mach numbers ranging from $10^{-3}$ to $0.4$. We find that for the lower Mach numbers the saturation efficiency of the dynamo, $(E_{\mathrm{mag}}/E_{\mathrm{kin}}){\mathrm{sat}}$, increases as the Mach number decreases. Even in the case when injection of energy is purely through longitudinal forcing modes, $(E{\mathrm{mag}}/E_{\mathrm{kin}})_{\mathrm{sat}}$ $\gtrsim 10^{-2}$ at a Mach number of $10^{-3}$. We apply our results to magnetic field amplification in the early Universe and predict that a turbulent dynamo can amplify primordial magnetic fields to $\gtrsim$ $10^{-16}$ Gauss on scales up to 0.1 pc and $\gtrsim$ $10^{-13}$ Gauss on scales up to 100 pc. This produces fields compatible with lower limits of the intergalactic magnetic field inferred from blazar $\gamma$-ray observations.

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R. Chirakkara, C. Federrath, P. Trivedi, et. al.
Thu, 21 Jan 21
45/56

Comments: 9 pages, 3 figures, 2 tables; accepted for publication in Physical Review Letters

Dust storm-enhanced gravity wave activity in the Martian thermosphere observed by MAVEN and implication for atmospheric escape [CL]

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http://arxiv.org/abs/2101.07698


Lower atmospheric global dust storms affect the small- and large-scale weather and variability of the whole Martian atmosphere. Analysis of the CO$_2$ density data from the Neutral Gas and Ion Mass Spectrometer instrument (NGIMS) on board NASA’s Mars Atmosphere Volatile EvolutioN (MAVEN) spacecraft show a remarkable increase of GW-induced density fluctuations in the thermosphere during the 2018 major dust storm with distinct latitude and local time variability. The mean thermospheric GW activity increases by a factor of two during the storm event. The magnitude of relative density perturbations is around 20% on average and 40% locally. One and a half months later, the GW activity gradually decreases. Enhanced temperature disturbances in the Martian thermosphere can facilitate atmospheric escape. For the first time, we estimate that, for a 20% and 40% GW-induced disturbances, the net increase of Jeans escape flux of hydrogen is a factor of 1.3 and 2, respectively.

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E. Yiğit, A. Medvedev, M. Benna, et. al.
Wed, 20 Jan 21
41/61

Comments: Accepted for publication in Geophysical Research Letters, 13 pages, 4 figures

A method to statistically characterize turbulent data with physically motivated parameters, illustrated on a centroid velocity map [GA]

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http://arxiv.org/abs/2101.07205


We investigate the potential of a recently proposed model for 3D compressible MHD turbulence (Chevillard et al. 2010; Durrive et al. 2021) to be used as a tool to characterize statistically 2D and 3D turbulent data. This model is parametrized by a dozen of free (intuitive, physically motivated) parameters, which control the statistics of the fields (density, velocity and magnetic fields). The present study is a proof of concept study: (i) we restrict ourselves to the incompressible hydrodynamical part of the model, (ii) we consider as data centroid velocity maps, and (iii) we let only three of the free parameters vary (namely the correlation length, the Hurst parameter and the intermittency parameter). Within this framework, we demonstrate that, given a centroid velocity map, we can find in an automated manner (i.e. by a Markov Chain Monte Carlo analysis) values of the parameters such that the model resembles the given map, i.e. which reproduces its statistics fairly well. Hence, thanks to this procedure, one may characterize statistically, and thus compare, various turbulent data. In other words, we show how this model may be used as a metric to compare observational or simulated data sets. In addition, because this model is numerically particularly fast (nearly 500 times faster than the numerical simulation we use to generate our reference data) it may be used as a surrogate model. Finally, by this process we also initiate the first systematic exploration of the parameter space of this model. Doing so, we show how the parameters impact the visual and the statistical properties of centroid velocity maps, and exhibit the correlations between the various parameters, providing new insight into the model.

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J. Durrive, P. Lesaffre, T. Ghosh, et. al.
Tue, 19 Jan 21
35/92

Comments: 15 pages, submitted to MNRAS

Surface effects and turbulent pressure. Assessing the Gas-$Γ_1$ and Reduced-$Γ_1$ empirical models [SSA]

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http://arxiv.org/abs/2101.06065


The use of the full potential of stellar seismology is made difficult by the improper modeling of the upper-most layers of solar-like stars and their influence on the modeled frequencies. Our knowledge on these \emph{surface effects} has improved thanks to the use of 3D hydrodynamical simulations but the calculation of eigenfrequencies relies on empirical models for the description of the Lagrangian perturbation of turbulent pressure: the reduced-$\Gamma_1$ model (RGM) and the gas-$\Gamma_1$ model (GGM). Starting from the fully compressible turbulence equations, we derive both the GGM and RGM models using a closure to model the flux of turbulent kinetic energy. It is found that both models originate from two terms: the source of turbulent pressure due to compression produced by the oscillations and the divergence of the flux of turbulent pressure. It is also demonstrated that they are both compatible with the adiabatic approximation but also imply a number of questionable assumptions mainly regarding mode physics. Among others hypothesis, one has to neglect the Lagrangian perturbation of the dissipation of turbulent kinetic energy into heat and the Lagrangian perturbation of buoyancy work.

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K. Belkacem, F. Kupka, J. Philidet, et. al.
Mon, 18 Jan 21
6/41

Comments: 7 pages, 1 figure. Accepted as a Letter in Astronomy and Astrophysic

Two Dimensional Turbulence in a Massless Fluid with a Relativistic Lattice Boltzmann Model [CL]

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http://arxiv.org/abs/2101.06187


We investigate a relativistic adaptation of the Lattice Boltzmann Method that reproduces the equations of motion for a turbulent, two-dimensional, massless hydrodynamic system. The classical Lattice Boltzmann Method and its extension to relativistic fluid dynamics is described. The numeric formulation is evaluated using a zero-averaged stirring force introduced into the numerics to induce turbulence, and the flow characteristics produced are compared to properties of a classical turbulent hydrodynamic flow. The model can reasonably be expected to offer quantitative simulations of electron fluid flows in graphene or Kagome lattices.

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M. Watson
Mon, 18 Jan 21
7/41

Comments: 28 pages, 11 Figures, Comments Welcome

The complex interplay between tidal inertial waves and zonal flows in differentially rotating stellar and planetary convective regions I. Free waves [SSA]

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http://arxiv.org/abs/2101.04656


Quantifying tidal interactions in close-in two-body systems is of prime interest since they have a crucial impact on the architecture and on the rotational history of the bodies. Various studies have shown that the dissipation of tides in either body is very sensitive to its structure and to its dynamics, like differential rotation which exists in the outer convective enveloppe of solar-like stars and giant gaseous planets. In particular, tidal waves may strongly interact with zonal flows at the so-called corotation resonances, where the wave’s Doppler-shifted frequency cancels out. We aim to provide a deep physical understanding of the dynamics of tidal inertial waves at corotation resonances, in the presence of differential rotation profiles typical of low-mass stars and giant planets. By developping an inclined shearing box, we investigate the propagation and the transmission of free inertial waves at corotation, and more generally at critical levels, which are singularities in the governing wave differential equation. Through the construction of an invariant called the wave action flux, we identify different regimes of wave transmission at critical levels, which are confirmed with a one-dimensional three-layer numerical model. We find that inertial waves can be either fully transmitted, strongly damped, or even amplified after crossing a critical level. The occurrence of these regimes depends on the assumed profile of differential rotation, on the nature as well as the latitude of the critical level, and on wave parameters such as the inertial frequency and the longitudinal and vertical wavenumbers. Waves can thus either deposit their action flux to the fluid when damped at critical levels, or they can extract action flux to the fluid when amplified at critical levels. Both situations could lead to significant angular momentum exchange between the tidally interacting bodies.

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A. Astoul, J. Park, S. Mathis, et. al.
Wed, 13 Jan 21
43/70

Comments: 25 pages, 12 figures, 4 tables, accepted for publication in Astronomy & Astrophysics

An intuitive parametric model for 3D compressible hydrodynamical and MHD turbulence [CL]

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http://arxiv.org/abs/2101.03447


An analytical model for three-dimensional incompressible turbulence was recently introduced in the hydrodynamics community which, with only a few parameters, shares many properties of experimental and numerical turbulence, notably intermittency (non-Gaussianity), the energy cascade (skewness), and vorticity alignment properties. In view of modeling astrophysical environments, we introduce a manner to extend to compressible fluids the three-dimensional turbulent velocity field model of Chevillard et al. (2010), as well as the three 3D turbulent magnetic field models of Durrive et al. (2020), following the same procedure based on the concept of multiplicative chaos. Our model provides a complementary tool to numerical simulations, as it enables us to generate very quickly fairly realistic velocity fields and magnetic fields, the statistics of which are controllable with intuitive parameters. Therefore our model will also provide a useful tool for observers in astrophysics. Finally, maybe even more than the model itself, it is the very procedure that matters the most: our model is modular, in the sense that it is constructed gradually, with intuitive and physically motivated steps, so that it is prone to many further improvements.

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J. Durrive, K. Ferrière and P. Lesaffre
Tue, 12 Jan 21
2/90

Comments: 15 pages, submitted to MNRAS

Geomagnetic semblance and dipolar-multipolar transition in top-heavy double-diffusive geodynamo models [CL]

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http://arxiv.org/abs/2101.03879


Convection in the liquid outer core of the Earth is expected to be driven by thermal and chemical density perturbations. The difference between the two buoyancy sources has been ignored in the majority of geodynamo models published to date. The main purpose of this study is to examine the impact of double-diffusive convection on magnetic field generation by means of three-dimensional global geodynamo models. We focus here on the “top-heavy” regime, when both thermal and compositional background gradients are destabilizing. We compute 79 numerical dynamo models spanning various fractionning of buoyancy sources. Using a linear eigensolver, we show that the onset of convection is facilitated by the addition of a second buoyancy source. The critical onset mode is similar to classical thermal Rossby waves observed with the codensity formalism. Using a rating parameter to quantify the morphological semblance of the models magnetic field with the geomagnetic field, we show that a good agreement can be attained for any partitioning of the convective input power. Next, we show that the transition between dipolar and multipolar dynamos strongly depends on the nature of the buoyancy forcing. A scale-dependent analysis of the force balance at work instead reveals that the dipole breakdown occurs when the ratio of inertia to Lorentz force at the dominant convective flow lengthscale reaches 0.5, independently of the distribution of input power between thermal and compositional buoyancies. The ratio of integrated kinetic to magnetic energy $E_k/E_m$ appears to be a reasonable proxy of this force ratio. Given that $E_k/E_m\approx 10^{-4}-10^{-3}$ in the Earth’s core, the geodynamo should operate far from this transition. It hence appears unlikely that the occurrence of geomagnetic reversals is related to dramatic and punctual changes of the amplitude of inertial forces in the Earth’s core.

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T. Tassin, T. Gastine and A. Fournier
Tue, 12 Jan 21
5/90

Comments: N/A

Linear stability analysis of the homogeneous Couette flow in a 2D isentropic compressible fluid [CL]

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http://arxiv.org/abs/2101.01696


In this paper, we study the linear stability properties of perturbations around the homogeneous Couette flow for a 2D isentropic compressible fluid in the domain $\mathbb{T}\times \mathbb{R}$. In the inviscid case there is a generic Lyapunov type instability for the density and the irrotational component of the velocity field. More precisely, we prove that their $L^2$ norm grows as $t^{1/2}$ and this confirms previous observations in the physics literature. Instead, the solenoidal component of the velocity field experience inviscid damping, meaning that it decays to zero even in the absence of viscosity. For a viscous compressible fluid, we show that the perturbations may have a transient growth of order $\nu^{-1/6}$ (with $\nu^{-1}$ being proportional to the Reynolds number) on a time-scale $\nu^{-1/3}$, after which it decays exponentially fast. This phenomenon is also called enhanced dissipation and our result appears to be the first to detect this mechanism for a compressible fluid, where an exponential decay for the density is not a priori trivial given the absence of dissipation in the continuity equation.

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P. Antonelli, M. Dolce and P. Marcati
Wed, 6 Jan 21
56/82

Comments: 39 pages. A preliminary analysis of the inviscid problem already appeared in our unpublished note arxiv.org/abs/2003.01694

Technique for separating velocity and density contributions in spectroscopic data and its application to studying turbulence and magnetic fields [GA]

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http://arxiv.org/abs/2012.15776


Based on the theoretical description of Position-Position-Velocity (PPV) statistics in Lazarian & Pogosyan (2000), we introduce a new technique called the Velocity Decomposition Algorithm (VDA) in separating the contribution of turbulent velocity from density fluctuations. Using MHD turbulence simulations, we demonstrate its promise in recovering the velocity caustics in various physical conditions and, in conjunction with the Velocity Gradient Technique (VGT), its prospects in accurately tracing the magnetic field based on pure velocity fluctuations. Employing the theoretical framework developed in Lazarian & Pogosyan (2004), we find that for localized clouds, the velocity fluctuations are most prominent at the wing part of the spectral line, and they dominate the density fluctuations. The same velocity dominance applies to extended HI regions with galactic rotations. Our numerical experiment demonstrates that velocity channels arising from the cold phase of atomic hydrogen (HI) are still strongly affected by the velocity caustics in small scales. We apply the VDA to the HI GALFA-DR2 data corresponding to the high-velocity cloud HVC186+19-114 and high latitude galactic diffuse HI data. Our study confirms the crucial role of velocity caustics in forming linear structures observed within PPV cubes. We discuss the implications of the VDA for both magnetic field studies and predicting polarized galactic emission that acts as the foreground for the Cosmic Microwave Background (CMB) studies. Besides, we address the controversy related to the nature of the filaments in HI channel maps and explain the importance of velocity caustics in the formation of structures in PPV data cubes. The VDA method will allow astronomers to obtain velocity caustics from almost every piece of spectroscopic PPV data and allows direct investigation of the turbulent velocity field in observations.

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K. Yuen, K. Ho and A. Lazarian
Fri, 1 Jan 21
59/103

Comments: 47 pages, 11 sections, 6 appendices, 25 figures in the main text, 7 figures in the appendices. Submitted to ApJ

Isostasy with Love: II Viscoelastic relaxation [EPA]

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http://arxiv.org/abs/2012.15226


In modern geodynamics, isostasy can be viewed either as the static equilibrium of the crust that minimizes deviatoric stresses, or as a dynamic process resulting from the viscous relaxation of the non-hydrostatic crustal shape. Paper~I gave a general formulation of Airy isostasy as a loading problem solved with Love numbers, and applied it to the case of minimum stress isostasy. In this sequel, the same framework is used to study Airy isostasy as the long-time evolution of a viscoelastic shell submitted to surface and internal loads. Isostatic ratios are defined in terms of time-dependent deviatoric Love numbers. Dynamic isostasy depends on the loading history, two flavours of which are the constant load applied at a specific time and the constant shape maintained by addition or removal of material at the compensation depth. Whereas the former model has no elastic analog, the latter is equivalent to elastic isostasy with zero deflection at the surface, which was shown in Paper~I to be dual to minimum stress isostasy. Viscoelastic and viscous approaches are completely equivalent. Isostatic models thus belong to two independent groups: the elastic/stationary approaches and the time-dependent approaches. If the shell is homogeneous, all models predict a similar compensation of large-scale gravity perturbations. If the shell rheology depends on depth, stationary models predict more compensation at long wavelengths, whereas time-dependent models result in negligible compensation. Analytical formulas for the isostatic ratios of an incompressible body with three homogeneous layers are given in complementary software.

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M. Beuthe
Fri, 1 Jan 21
86/103

Comments: 42 pages, 8 figures, 4 tables

Isostasy with Love: II Viscoelastic relaxation [EPA]

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http://arxiv.org/abs/2012.15226


In modern geodynamics, isostasy can be viewed either as the static equilibrium of the crust that minimizes deviatoric stresses, or as a dynamic process resulting from the viscous relaxation of the non-hydrostatic crustal shape. Paper~I gave a general formulation of Airy isostasy as a loading problem solved with Love numbers, and applied it to the case of minimum stress isostasy. In this sequel, the same framework is used to study Airy isostasy as the long-time evolution of a viscoelastic shell submitted to surface and internal loads. Isostatic ratios are defined in terms of time-dependent deviatoric Love numbers. Dynamic isostasy depends on the loading history, two flavours of which are the constant load applied at a specific time and the constant shape maintained by addition or removal of material at the compensation depth. Whereas the former model has no elastic analog, the latter is equivalent to elastic isostasy with zero deflection at the surface, which was shown in Paper~I to be dual to minimum stress isostasy. Viscoelastic and viscous approaches are completely equivalent. Isostatic models thus belong to two independent groups: the elastic/stationary approaches and the time-dependent approaches. If the shell is homogeneous, all models predict a similar compensation of large-scale gravity perturbations. If the shell rheology depends on depth, stationary models predict more compensation at long wavelengths, whereas time-dependent models result in negligible compensation. Analytical formulas for the isostatic ratios of an incompressible body with three homogeneous layers are given in complementary software.

Read this paper on arXiv…

M. Beuthe
Fri, 1 Jan 21
29/103

Comments: 42 pages, 8 figures, 4 tables

Technique for separating velocity and density contributions in spectroscopic data and its application to studying turbulence and magnetic fields [GA]

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http://arxiv.org/abs/2012.15776


Based on the theoretical description of Position-Position-Velocity (PPV) statistics in Lazarian & Pogosyan (2000), we introduce a new technique called the Velocity Decomposition Algorithm (VDA) in separating the contribution of turbulent velocity from density fluctuations. Using MHD turbulence simulations, we demonstrate its promise in recovering the velocity caustics in various physical conditions and, in conjunction with the Velocity Gradient Technique (VGT), its prospects in accurately tracing the magnetic field based on pure velocity fluctuations. Employing the theoretical framework developed in Lazarian & Pogosyan (2004), we find that for localized clouds, the velocity fluctuations are most prominent at the wing part of the spectral line, and they dominate the density fluctuations. The same velocity dominance applies to extended HI regions with galactic rotations. Our numerical experiment demonstrates that velocity channels arising from the cold phase of atomic hydrogen (HI) are still strongly affected by the velocity caustics in small scales. We apply the VDA to the HI GALFA-DR2 data corresponding to the high-velocity cloud HVC186+19-114 and high latitude galactic diffuse HI data. Our study confirms the crucial role of velocity caustics in forming linear structures observed within PPV cubes. We discuss the implications of the VDA for both magnetic field studies and predicting polarized galactic emission that acts as the foreground for the Cosmic Microwave Background (CMB) studies. Besides, we address the controversy related to the nature of the filaments in HI channel maps and explain the importance of velocity caustics in the formation of structures in PPV data cubes. The VDA method will allow astronomers to obtain velocity caustics from almost every piece of spectroscopic PPV data and allows direct investigation of the turbulent velocity field in observations.

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K. Yuen, K. Ho and A. Lazarian
Fri, 1 Jan 21
94/103

Comments: 47 pages, 11 sections, 6 appendices, 25 figures in the main text, 7 figures in the appendices. Submitted to ApJ

Effects of latitude-dependent gravity wave source variations on the middle and upper atmosphere [CL]

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http://arxiv.org/abs/2012.12829


Atmospheric gravity waves (GWs) are generated in the lower atmosphere by various weather phenomena. They propagate upward, carry energy and momentum to higher altitudes, and appreciably influence the general circulation upon depositing them in the middle and upper atmosphere. We use a three-dimensional first-principle general circulation model (GCM) with an implemented nonlinear whole atmosphere GW parameterization to study the global climatology of wave activity and produced effects at altitudes up to the upper thermosphere. The numerical experiments were guided by the GW momentum fluxes and temperature variances as measured in 2010 by the SABER (Sounding of the Atmosphere using Broadband Emission Radiometry) instrument onboard NASA’s TIMED (Thermosphere Ionosphere Mesosphere Energetics Dynamics) satellite. This includes the latitudinal dependence and magnitude of GW activity in the lower stratosphere for the boreal summer season. The modeling results were compared to the SABER temperature and total absolute momentum flux, and Upper Atmosphere Research Satellite (UARS) data in the mesosphere and lower thermosphere. Simulations suggest that, in order to reproduce the observed circulation and wave activity in the middle atmosphere, smaller than the measured GW fluxes have to be used at the source level in the lower atmosphere. This is because observations contain a broader spectrum of GWs, while parameterizations capture only a portion relevant to the middle and upper atmosphere dynamics. Accounting for the latitudinal variations of the source appreciably improves simulations.

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E. Yiğit, A. Medvedev and M. Ern
Thu, 24 Dec 20
45/73

Comments: Submitted to Frontiers in Astronomy and Space Sciences. Research Topic: “Coupling Processes in Terrestrial and Planetary Atmospheres”

Large-scale vortices and zonal flows in spherical rotating convection [CL]

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http://arxiv.org/abs/2012.12061


Motivated by understanding the dynamics of stellar and planetary interiors, we have performed a set of direct numerical simulations of Boussinesq convection in a rotating full sphere. The domain is internally heated with fixed temperature and stress-free boundary conditions, but fixed heat flux and no-slip boundary conditions are also briefly considered. We particularly focus on the large scale coherent structures and the mean zonal flows that can develop in the system. At Prandtl number of unity, as the thermal forcing (measured by the Rayleigh number) is increased above the value for the onset of convection, we find a relaxation oscillation regime, followed by a geostrophic turbulence regime. Beyond this we see for the first time the existence of large scale coherent vortices that form on the rotation axis. All regime boundaries are well-described by critical values of the convective Rossby number $Ro_c$, with transitions from oscillatory to geostrophic turbulence, and then to the large scale vortex regime at values $Ro_c\approx 0.2$ and $Ro_c\approx 1.5$ respectively. The zonal flow is controlled by the convective Rossby number and changes its direction when the flow transitions from the geostrophic turbulence regime to the large-scale vortex regime. While the non-zonal flow speed and heat transfer can be described by the so-called inertial scaling in the geostrophic turbulence regime, the formation of large-scale vortices appears to reduce both the non-zonal flow speed and the efficiency of convective heat transfer.

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Y. Lin and A. Jackson
Wed, 23 Dec 20
33/72

Comments: 23 pages, 17 figures, accepted for publication in J. Ffluid Mech

Radiative heating achieves the ultimate regime of thermal convection [CL]

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http://arxiv.org/abs/2012.10935


The absorption of light or radiation drives turbulent convection inside stars, supernovae, frozen lakes and the Earth’s mantle. In these contexts, the goal of laboratory and numerical studies is to determine the relation between the internal temperature gradients and the heat flux transported by the turbulent flow. This is the constitutive law of turbulent convection, to be input into large-scale models of such natural flows. However, in contrast with the radiative heating of natural flows, laboratory experiments have focused on convection driven by heating and cooling plates: the heat transport is then severely restricted by boundary layers near the plates, which prevents the realization of the mixing-length scaling-law used in evolution models of geophysical and astrophysical flows. There is therefore an important discrepancy between the scaling-laws measured in laboratory experiments and those used eg. in stellar evolution models. Here we provide experimental and numerical evidence that radiatively driven convection spontaneously achieves the mixing-length scaling regime, also known as the `ultimate’ regime of thermal convection. This constitutes the first clear observation of this regime of turbulent convection. Our study therefore bridges the gap between models of natural flows and laboratory experiments. It opens an experimental avenue for a priori determinations of the constitutive laws to be implemented into models of geophysical and astrophysical flows, as opposed to empirical fits of these constitutive laws to the scarce observational data.

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S. Lepot, S. Aumaître and B. Gallet
Tue, 22 Dec 20
86/89

Comments: N/A

Superfluid dynamics in neutron star crusts: the Iordanskii force and chemical gauge covariance [HEAP]

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http://arxiv.org/abs/2012.10288


We present a geometrical derivation of the relativistic dynamics of the superfluid inner crust of a neutron star. The resulting model is analogous to the Hall-Vinen-Bekarevich-Khalatnikov hydrodynamics for a single-component superfluid at finite temperature, but particular attention should be paid to the fact that some fraction of the neutrons are locked to the motion of the protons in nuclei. This gives rise to an ambiguity in the definition of the two currents (the normal and the superfluid one) on which the model is built, a problem that manifests itself as a chemical gauge freedom of the theory. To ensure chemical gauge covariance of the hydrodynamic model, the phenomenological equation of motion for a quantized vortex should contain an extra transverse force, that is the relativistic version of the Iordanskii force discussed in the context of superfluid Helium. Hence, we extend the mutual friction model of Langlois et al. (1998) to account for the possible presence of this Iordanskii-like force. Furthermore, we propose that a better understanding of the (still not completely settled) controversy around the presence of the Iordanskii force in superfluid Helium, as well as in neutron stars, may be achieved by considering that the different incompatible results present in the literature pertain to two, opposite, dynamical regimes of the fluid system.

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L. Gavassino, M. Antonelli and B. Haskell
Mon, 21 Dec 20
39/75

Comments: 35 pages, 1 figure

Interaction of large- and small-scale dynamos in isotropic turbulent flows from GPU-accelerated simulations [CL]

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http://arxiv.org/abs/2012.08758


Magnetohydrodynamical (MHD) dynamos emerge in many different astrophysical situations where turbulence is present, but the interaction between large-scale (LSD) and small-scale dynamos (SSD) is not fully understood. We performed a systematic study of turbulent dynamos driven by isotropic forcing in isothermal MHD with magnetic Prandtl number of unity, focusing on the exponential growth stage. Both helical and non-helical forcing was employed to separate the effects of LSD and SSD in a periodic domain. Reynolds numbers (Rm) up to $\approx 250$ were examined and multiple resolutions used for convergence checks. We ran our simulations with the Astaroth code, designed to accelerate 3D stencil computations on graphics processing units (GPUs) and to employ multiple GPUs with peer-to-peer communication. We observed a speedup of $\approx 35$ in single-node performance compared to the widely used multi-CPU MHD solver Pencil Code. We estimated the growth rates both from the averaged magnetic fields and their power spectra. At low Rm, LSD growth dominates, but at high Rm SSD appears to dominate in both helically and non-helically forced cases. Pure SSD growth rates follow a logarithmic scaling as a function of Rm. Probability density functions of the magnetic field from the growth stage exhibit SSD behaviour in helically forced cases even at intermediate Rm. We estimated mean-field turbulence transport coefficients using closures like the second-order correlation approximation (SOCA). They yield growth rates similar to the directly measured ones and provide evidence of $\alpha$ quenching. Our results are consistent with the SSD inhibiting the growth of the LSD at moderate Rm, while the dynamo growth is enhanced at higher Rm.

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M. Väisälä, J. Pekkilä, M. Käpylä, et. al.
Thu, 17 Dec 20
45/85

Comments: 22 pages, 23 figures, 2 tables, Accepted for publication in the Astrophysical Journal

Effects of shell thickness on cross-helicity generation in convection-driven spherical dynamos [CL]

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http://arxiv.org/abs/2012.06929


The relative importance of the helicity and cross-helicity electromotive dynamo effects for self-sustained magnetic field generation by chaotic thermal convection in rotating spherical shells is investigated as a function of shell thickness. Two distinct branches of dynamo solutions are found to coexist in direct numerical simulations for shell aspect ratios between 0.25 and 0.6 – a mean-field dipolar regime and a fluctuating dipolar regime. The properties characterising the coexisting dynamo attractors are compared and contrasted, including differences in temporal behavior and spatial structures of both the magnetic field and rotating thermal convection. The helicity $\alpha$-effect and the cross-helicity $\gamma$-effect are found to be comparable in intensity within the fluctuating dipolar dynamo regime, where their ratio does not vary significantly with the shell thickness. In contrast, within the mean-field dipolar dynamo regime the helicity $\alpha$-effect dominates by approximately two orders of magnitude and becomes stronger with decreasing shell thickness.

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L. Silva, P. Gupta, D. MacTaggart, et. al.
Tue, 15 Dec 20
107/136

Comments: Fluids (ISSN 2311-5521; CODEN: FLUICM); Accepted 2020-12-12

Multiple zonal jets in a turbulent Jovian dynamo model [EPA]

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http://arxiv.org/abs/2012.06438


The ongoing NASA’s Juno mission puts new constraints on the internal dynamics of Jupiter. Data gathered by its onboard magnetometer reveal a dipole-dominated surface magnetic field accompanied by strong localised magnetic flux patches. The gravity measurements indicate that the fierce surface zonal jets extend several thousands of kilometers below the cloud level before rapidly decaying below $0.94-0.96\,R_J$, $R_J$ being the mean Jovian radius at the one bar level. Several internal models suggest an intricate internal structure with a thin intermediate region in which helium would segregate from hydrogen, forming a compositionally-stratified layer. Here, we develop the first global Jovian dynamo which incorporates an intermediate stably-stratified layer between $0.82\,R_J$ and $0.86\,R_J$. Analysing the energy balance reveals that the magnetic energy is almost one order of magnitude larger than kinetic energy in the metallic region, while most of the kinetic energy is pumped into zonal motions in the molecular envelope. Those result from the different underlying force hierarchy with a triple balance between Lorentz, Archimedean and ageostrophic Coriolis forces in the metallic core and inertia, buoyancy and ageostrophic Coriolis forces controlling the external layers. The simulation presented here is the first to demonstrate that multiple zonal jets and Jupiter-like dynamo action can be consolidated in a global simulation. The inclusion of an stable layer is a necessary ingredient that allows zonal jets to develop in the outer envelope without contributing to the dynamo action in the deeper metallic region. Stable stratification however also smooths out the small-scale features of the magnetic field by skin effect. These constraints suggest that possible stable layers in Jupiter should be located much closer to the surface ($0.9-0.95\,R_J$).

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T. Gastine and J. Wicht
Mon, 14 Dec 20
13/74

Comments: 22 pages, 16 figures, 2 tables, submitted to Icarus

Generation of mean flows in rotating anisotropic turbulence: The case of solar near-surface shear layer [SSA]

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http://arxiv.org/abs/2012.06343


The radial gradient of the rotation rate in the near-surface shear layer (NSSL) of the Sun is independent of latitude and radius. Theoretical mean-field models have been successful in explaining this property of the solar NSSL, while global direct convection models have been unsuccessful. We investigate reason for this discrepancy by measuring the mean flows, Reynolds stress, and turbulent transport coefficients under NSSL conditions. Simulations have minimal ingredients. These ingredients are inhomogeneity due to boundaries, anisotropic turbulence, and rotation. Parameters of the simulations are chosen such they match the weakly rotationally constrained NSSL. The simulations probe locally Cartesian patches of the star at a given depth and latitude. The depth of the patch is varied by changing the rotation rate such that the resulting Coriolis numbers<1. We measure the turbulent transport coefficient relevant for the non-diffusive and diffusive parts of the Reynolds stress and compare them with predictions of current mean-field theories. A negative radial gradient of mean flow similar to the solar NSSL is generated only at the equator where meridional flows are absent. At other latitudes the meridional flow is comparable to the mean flow corresponding to differential rotation. We also find that meridional components of the Reynolds stress cannot be ignored. Additionally, we find that the turbulent viscosity is quenched by rotation by about 50\% from the surface to the bottom of the NSSL. Our local simulations do not validate the explanation for the generation of the NSSL from mean-field theory where meridional stresses are neglected. However, the rotational dependence of turbulent viscosity in our simulations is in good agreement with theoretical prediction. Our results are in qualitative agreement with global convection simulations in that a NSSL obtained near the equator.

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A. Barekat, M. Käpylä, P. Käpylä, et. al.
Mon, 14 Dec 20
54/74

Comments: N/A

Calibrating Core Overshooting Parameters With Two-dimensional Hydrodynamical Simulations [SSA]

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http://arxiv.org/abs/2012.05262


The extent of mixed regions around convective zones is one of the biggest uncertainties in stellar evolution. 1D overshooting descriptions introduce a free parameter ($f_{ov}$) that is in general not well constrained from observations. Especially in small central convective regions the value is highly uncertain due to its tight connection to the pressure scale height. Long-term multi-dimensional hydrodynamic simulations can be used to study the size of the overshooting region and the involved mixing processes. Here we show how one can calibrate an overshooting parameter by performing 2D Maestro simulations of Zero-Age-Main-Sequence stars ranging from $1.3$ to $3.5 M_\odot$. The simulations cover the convective cores of the stars and a large fraction of the surrounding radiative envelope. We follow the convective flow for at least 20 convective turnover times, while the longest simulation covers 430 turnover time scales. This allows us to study how the mixing as well as the convective boundary evolve with time, and how the resulting entrainment can be interpreted in terms of overshooting parameters. We find that increasing the overshooting parameter $f_{ov}$ beyond a certain value in the initial model of our simulations, changes the mixing behaviour completely. This result can be used to put limits on the overshooting parameter. We find $0.010 < f_{ov} < 0.017$ to be in good agreement with our simulations of a $3.5 M_\odot$ mass star. We also identify a diffusive mixing component due to internal gravity waves (IGW) that is active throughout the convectively stable layer, but likely overestimated in our simulations. Furthermore, applying our calibration method to simulations of less massive stars suggests a need for a mass-dependent overshooting description where the mixing in terms of the pressure scale height is reduced for small convective cores.

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J. Higl, E. Mueller and A. Weiss
Fri, 11 Dec 20
71/75

Comments: Accepted for publication in A&A

Chaotic and turbulent temperature fluctuations in atmospheric free convection [CL]

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http://arxiv.org/abs/2002.04562


It is shown, using results of direct numerical simulations, laboratory experiments, measurements in the atmospheric boundary layer, satellite infrared radiances data, the planetary-scale surface-air and tropospheric data, that the temperature fluctuations in atmospheric free convection can be well described by the spatio-temporal distributed chaos approach based on the Bolgiano-Obukhov phenomenology. A possibility of analogous consideration of the atmospheric dynamics on other planets (Mars, Jupiter and Saturn) has been briefly discussed using the data obtained with the Phoenix lander and the infrared observations.

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A. Bershadskii
Wed, 9 Dec 20
18/80

Comments: Extended (new data have been added)

Reconnection-controlled decay of magnetohydrodynamic turbulence and the role of invariants [CL]

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http://arxiv.org/abs/2012.01393


We present a new theoretical picture of magnetically dominated, decaying turbulence in the absence of a mean magnetic field. We demonstrate that such turbulence is governed by the reconnection of magnetic structures, and not by ideal dynamics, as has previously been assumed. We obtain predictions for the magnetic-energy decay laws by proposing that turbulence decays on reconnection timescales, while respecting the conservation of certain integral invariants representing topological constraints satisfied by the reconnecting magnetic field. As is well known, the magnetic helicity is such an invariant for initially helical field configurations, but does not constrain non-helical decay, where the volume-averaged magnetic-helicity density vanishes. For such a decay, we propose a new integral invariant, analogous to the Loitsyansky and Saffman invariants of hydrodynamic turbulence, that expresses the conservation of the random (scaling as $\mathrm{volume}^{1/2}$) magnetic helicity contained in any sufficiently large volume. Our treatment leads to novel predictions for the magnetic-energy decay laws: in particular, while we expect the canonical $t^{-2/3}$ power law for helical turbulence when reconnection is fast (i.e., plasmoid-dominated or stochastic), we find a shallower $t^{-4/7}$ decay in the slow `Sweet-Parker’ reconnection regime, in better agreement with existing numerical simulations. For non-helical fields, for which there currently exists no definitive theory, we predict power laws of $t^{-10/9}$ and $t^{-20/17}$ in the fast- and slow-reconnection regimes, respectively. We formulate a general principle of decay of turbulent systems subject to conservation of Saffman-like invariants, and propose how it may be applied to MHD turbulence with a strong mean magnetic field and to isotropic MHD turbulence with initial equipartition between the magnetic and kinetic energies.

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D. Hosking and A. Schekochihin
Mon, 7 Dec 20
29/69

Comments: 26 pages, 14 figures

Reconnection-controlled decay of magnetohydrodynamic turbulence and the role of invariants [CL]

Posted on by

http://arxiv.org/abs/2012.01393


We present a new theoretical picture of magnetically dominated, decaying turbulence in the absence of a mean magnetic field. We demonstrate that such turbulence is governed by the reconnection of magnetic structures, and not by ideal dynamics, as has previously been assumed. We obtain predictions for the magnetic-energy decay laws by proposing that turbulence decays on reconnection timescales, while respecting the conservation of certain integral invariants representing topological constraints satisfied by the reconnecting magnetic field. As is well known, the magnetic helicity is such an invariant for initially helical field configurations, but does not constrain non-helical decay, where the volume-averaged magnetic-helicity density vanishes. For such a decay, we propose a new integral invariant, analogous to the Loitsyansky and Saffman invariants of hydrodynamic turbulence, that expresses the conservation of the random (scaling as $\mathrm{volume}^{1/2}$) magnetic helicity contained in any sufficiently large volume. Our treatment leads to novel predictions for the magnetic-energy decay laws: in particular, while we expect the canonical $t^{-2/3}$ power law for helical turbulence when reconnection is fast (i.e., plasmoid-dominated or stochastic), we find a shallower $t^{-4/7}$ decay in the slow `Sweet-Parker’ reconnection regime, in better agreement with existing numerical simulations. For non-helical fields, for which there currently exists no definitive theory, we predict power laws of $t^{-10/9}$ and $t^{-20/17}$ in the fast- and slow-reconnection regimes, respectively. We formulate a general principle of decay of turbulent systems subject to conservation of Saffman-like invariants, and propose how it may be applied to MHD turbulence with a strong mean magnetic field and to isotropic MHD turbulence with initial equipartition between the magnetic and kinetic energies.

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D. Hosking and A. Schekochihin
Thu, 3 Dec 20
8/81

Comments: 26 pages, 14 figures

Smoke-charged vortices in the stratosphere generated by wildfires and their behaviour in both hemispheres : comparing Australia 2020 to Canada 2017 [CL]

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http://arxiv.org/abs/2011.13239


The two most intense wildfires of the last decade that took place in Canada in 2017 and Australia in 2019-2020 were followed by large injections of smoke in the stratosphere due to pyroconvection. It was discovered by Khaykin et al. (2020, doi:10.1038/s43247-020-00022-5) and Kablick et al. (2020, doi:10.1029/2020GL088101) that, after the Australian event, part of this smoke self-organized as anticyclonic confined vortices that rose in the mid-latitude stratosphere up to 35 km. Based on CALIOP observations and the ERA5 reanalysis, this new study analyzes the Canadian case and find, similarly, that a large plume penetrated the stratosphere by 12 August 2017 and got trapped within a meso-scale anticyclonic structure which travelled across the Atlantic. It then broke into three offsprings that could be followed until mid-October performing three round the world journeys and rising up to 23 km. We analyze the dynamical structure of the vortices produced by these two wildfires and demonstrate how they are maintained by the assimilation of data from instruments measuring the signature of the vortices in the temperature and ozone field. We propose that these vortices can be seen as bubbles of low absolute potential vorticity and smoke carried vertically across the stratification from the troposphere inside the middle stratosphere by their internal heating, against the descending flux of the Brewer-Dobson circulation.

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H. Lestrelin, B. Legras, A. Podglajen, et. al.
Mon, 30 Nov 20
34/117

Comments: Submitted to Atmospheric Chemistry and Physics

Phase Shift of Planetary Waves and Wave–Jet Resonance on Tidally Locked Planets [CL]

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http://arxiv.org/abs/2011.14553


Recent studies found that atmospheric superrotation (i.e., west-to-east winds over the equator) on tidally locked planets can modify the phase of planetary waves. But, a clear relationship between the superrotation and the magnitude of the phase shift was not examined. In this study, we re-investigate this problem using a two-dimensional (2D) linear shallow water model with a specified uniform zonal flow. We find that the degree of the phase shift is a monotonic but nonlinear function of the strength of the mean flow, and the phase shift has two limits of -$\pi$ and +$\pi$. The existence of these limits can be explained using the energy balance of the whole system. We further show that a resonance between the Rossby wave and the mean flow occurs when the speed of an eastward jet approaches to the westward phase speed of the Rossby wave, or a resonance between the Kelvin wave and the mean flow happens when the speed of a westward jet approaches to the eastward phase speed of the Kelvin wave. The resonance mechanism is the same as that found in the previous studies on Earth and hot Jupiters. Moreover, in the spin-up period of a 3D global atmospheric general circulation simulation for tidally locked rocky planet, we also find these two phenomena: phase shift and wave–jet resonance. This study improves the understanding of wave–mean flow interactions on tidally locked planets.

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S. Wang and J. Yang
Tue, 1 Dec 20
39/108

Comments: N/A

Gone with the headwind : planetesimals on eccentric orbits erode rapidly [EPA]

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http://arxiv.org/abs/2011.14431


We investigate the possibility of erosion of planetesimals in a protoplanetary disk.
We use theory and direct numerical simulations (Lattice Boltzmann Method) to calculate the erosion of large — much larger than mean-free-path of gas molecules — bodies of different shapes in flows. We find that erosion follows a universal power-law in time, at intermediate times, independent of the Reynolds number of the flow and the initial shape of the body. Consequently, we estimate that planetesimals in eccentric orbits, of even very small eccentricity, rapidly (in about hundred years) erodes away if the semi-major axis of their orbit lies in the inner disk — less than about $10$ AU. Even planetesimals in circular orbits erode away in approximately ten thousand years if the semi-major axis of their orbits are $\lessapprox 0.6$AU.

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L. Cedenblad, N. Schaffer, A. Johansen, et. al.
Tue, 1 Dec 20
79/108

Comments: N/A

Gas giant-like zonal jets in the laboratory [CL]

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http://arxiv.org/abs/2011.12178


This paper is associated with a poster winner of a 2019 American Physical Society Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, this https URL.

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D. Lemasquerier, B. Favier and M. Bars
Wed, 25 Nov 2020
22/65

Comments: N/A

Remote determination of the shape of Jupiter's vortices from laboratory experiments [EPA]

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http://arxiv.org/abs/2011.11279


Jupiter’s dynamics shapes its cloud patterns but remains largely unknown below this natural observational barrier. Unraveling the underlying three-dimensional flows is thus a primary goal for NASA’s ongoing Juno mission that was launched in 2011. Here, we address the dynamics of large Jovian vortices using laboratory experiments complemented by theoretical and numerical analyses. We determine the generic force balance responsible for their three-dimensional pancake-like shape. From this, we define scaling laws for their horizontal and vertical aspect ratios as a function of the ambient rotation, stratification and zonal wind velocity. For the Great Red Spot in particular, our predicted horizontal dimensions agree well with measurements at the cloud level since the Voyager mission in 1979. We additionally predict the Great Red Spot’s thickness, inaccessible to direct observation: it has surprisingly remained constant despite the observed horizontal shrinking. Our results now await comparison with upcoming Juno observations.

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D. Lemasquerier, G. Facchini, B. Favier, et. al.
Tue, 24 Nov 2020
65/83

Comments: N/A

Wave-Driven Shocks in Stellar Outbursts: Dynamics, Envelope Heating, and Nascent Blastwaves [SSA]

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http://arxiv.org/abs/2011.08861


We address the shocks from acoustic pulses and wave trains in general one-dimensional flows, with an emphasis on the application to super-Eddington outbursts in massive stars. Using approximate adiabatic invariants, we generalize the classical equal-area technique in its integral and differential forms. We predict shock evolution for the case of an initially sinusoidal but finite wave train, with separate solutions for internal shocks and head or tail shocks, and demonstrate detailed agreement with numerical simulations. Our internal shock solution motivates improved expressions for the shock heating rate. Our solution for head and tail shocks demonstrates that these preserve dramatically more wave energy to large radii and have a greater potential for the direct ejection of matter. This difference highlights the importance of the waveform for shock dynamics. Our weak-shock analysis predicts when shocks will become strong and provides a basis from which this transition can be addressed. We use it to estimate the mass ejected by sudden sound pulses and weak central explosions.

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C. Matzner and S. Ro
Thu, 19 Nov 20
44/83

Comments: 11 pages, 5 figures. ApJ, accepted

Variable energy flux in turbulence [CL]

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http://arxiv.org/abs/2011.07291


In three-dimensional hydrodynamic turbulence forced at large length scales, a constant energy flux $ \Pi_u $ flows from large scales to intermediate scales, and then to small scales. It is well known that for multiscale energy injection and dissipation, the energy flux $\Pi_u$ varies with scales. In this review we describe this principle and show how this general framework is useful for describing a variety of turbulent phenomena. Compared to Kolmogorov’s spectrum, the energy spectrum steepens in turbulence involving quasi-static magnetofluid, Ekman friction, stable stratification, magnetohydrodynamics, and solution with dilute polymer. However, in turbulent thermal convection, in unstably stratified turbulence such as Rayleigh-Taylor turbulence, and in shear turbulence, the energy spectrum has an opposite behaviour due to an increase of energy flux with wavenumber. In addition, we briefly describe the role of variable energy flux in quantum turbulence, in binary-fluid turbulence including time-dependent Landau-Ginzburg and Cahn-Hillianrd equations, and in Euler turbulence.

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M. Verma
Wed, 18 Nov 20
66/79

Comments: 69 pages

Deep convection-driven vortex formation on Jupiter and Saturn [EPA]

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http://arxiv.org/abs/2011.07263


The surface of both Jupiter and Saturn has magnificent vortical storms which help shape the dynamic nature of their atmospheres. Land- and space-based observational campaigns over time have established several properties of these vortices, with some being similar between the two planets, while others are different. Shallow-water hydrodynamics, where the vortices are treated as shallow weather-layer phenomenon, is commonly evoked for explaining their formation and properties. Here we report novel formation mechanisms for vortices where the primary driving mechanism is the deep planetary convection occurring in these planets. Using three dimensional simulations of turbulent convection in rotating spherical shells, we propose two ideas: (1) rotating turbulent convection generates deep axially-aligned cyclones and anticyclones; (2) a deep planetary dynamo acts to promote additional anticyclones, some as large as Jupiter’s Great Red Spot, in an overlying atmospheric layer. We use these ideas to interpret several observational properties of vortices on Jupiter and Saturn.

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R. Yadav, M. Heimpel and J. Bloxham
Tue, 17 Nov 20
48/83

Comments: 16 Pages, 3 main and 7 supplementary figures, 2 animations on youtube

Mode Conversion and Period Doubling at Plasma-$β$ Unity in an Alfvén-Wave Experiment with Liquid Rubidium [CL]

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http://arxiv.org/abs/2010.15565


We report Alfv\’en-wave experiments with liquid rubidium at the Dresden High Magnetic Field Laboratory (HLD). Reaching up to 63 T, the pulsed magnetic field exceeds the critical value of 54 T at which the Alfv\’en speed becomes equal to the sound speed (plasma-$\beta$ unity). At this threshold we observe a period doubling of an applied 8 kHz CW excitation, a clear footprint for a parametric resonance between magnetosonic waves and Alfv\’en waves.

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F. Stefani, J. Forbriger, T. Gundrum, et. al.
Fri, 30 Oct 20
59/74

Comments: 5 pages, 4 figures

The impact of magnetic fields on momentum transport and saturation of shear-flow instability by stable modes [CL]

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http://arxiv.org/abs/2010.11198


The Kelvin-Helmholtz (KH) instability of a shear layer with an initially-uniform magnetic field in the direction of flow is studied in the framework of 2D incompressible magnetohydrodynamics with finite resistivity and viscosity using direct numerical simulations. The shear layer evolves freely, with no external forcing, and thus broadens in time as turbulent stresses transport momentum across it. As with KH-unstable flows in hydrodynamics, the instability here features a conjugate stable mode for every unstable mode in the absence of dissipation. Stable modes are shown to transport momentum up its gradient, shrinking the layer width whenever they exceed unstable modes in amplitude. In simulations with weak magnetic fields, the linear instability is minimally affected by the magnetic field, but enhanced small-scale fluctuations relative to the hydrodynamic case are observed. These enhanced fluctuations coincide with increased energy dissipation and faster layer broadening, with these features more pronounced in simulations with stronger fields. These trends result from the magnetic field reducing the effects of stable modes relative to the transfer of energy to small scales. As field strength increases, stable modes become less excited and thus transport less momentum against its gradient. Furthermore, the energy that would otherwise transfer back to the driving shear due to stable modes is instead allowed to cascade to small scales, where it is lost to dissipation. Approximations of the turbulent state in terms of a reduced set of modes are explored. While the Reynolds stress is well-described using just two modes per wavenumber at large scales, the Maxwell stress is not.

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A. Fraser, P. Terry, E. Zweibel, et. al.
Fri, 23 Oct 20
59/67

Comments: 39 pages, 17 figures, preprint format

Extremely High-Order Convergence in Simulations of Relativistic Stars [CL]

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http://arxiv.org/abs/2010.05126


We provide a road towards obtaining gravitational waveforms from inspiraling material binaries with an accuracy viable for third-generation gravitational wave detectors, without necessarily advancing computational hardware or massively-parallel software infrastructure. We demonstrate a proof-of-principle 1+1-dimensional numerical implementation that exhibits up to 7th-order convergence for highly dynamic barotropic stars in curved spacetime, and numerical errors up to 6 orders of magnitude smaller than a standard method. Aside from Runge’s phenomenon, there are no obvious fundamental obstacles to obtaining convergence of even higher order. The implementation uses a novel surface-tracking method, where the surface is evolved and high-order accurate boundary conditions are imposed there. Computational memory does not need to be allocated to fluid variables in the vacuum region of spacetime. We anticipate the application of this new method to full $3! +! 1$-dimensional simulations of the inspiral phase of compact binary systems with at least one material body. The additional challenge of a deformable surface must be addressed in multiple spatial dimensions, but it is also an opportunity to input more precise surface tension physics.

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J. Westernacher-Schneider
Tue, 13 Oct 20
71/97

Comments: Pdf ~1 Mb. 13 page body, 2 pages of appendices. Journal submission will be delayed to allow for feedback from readers. Video content available at this https URL

Polydisperse Streaming Instability I. Tightly coupled particles and the terminal velocity approximation [EPA]

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http://arxiv.org/abs/2010.01145


We introduce a polydisperse version of the streaming instability, where the dust component is treated as a continuum of sizes. We show that its behaviour is remarkably different from the monodisperse streaming instability. We focus on tightly coupled particles in the terminal velocity approximation and show that unstable modes that grow exponentially on a dynamical time scale exist. However, for dust to gas ratios much smaller than unity they are confined to radial wave numbers that are a factor $\sim 1/\overline{\rm St}$ larger than where the monodisperse streaming instability growth rates peak. Here $\overline{\rm St} \ll 1$ is a suitable average Stokes number for the dust size distribution. For dust to gas ratios larger than unity, polydisperse modes that grow on a dynamical time scale are found as well, similar as for the monodisperse streaming instability and at similarly large wave numbers. At smaller wave numbers, where the classical monodisperse streaming instability shows secular growth, no growing polydisperse modes are found under the terminal velocity approximation. Outside the region of validity for the terminal velocity approximation, we have found unstable epicyclic modes that grow on $\sim 10^4$ dynamical time scales.

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S. Paardekooper, C. McNally and F. Lovascio
Tue, 6 Oct 20
80/85

Comments: 17 pages, 10 figures, 1 table. Submitted

Dynamic mode decomposition to retrieve torsional Alfvén waves [CL]

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http://arxiv.org/abs/2009.13095


Dynamic mode decomposition (DMD) is utilised to identify the intrinsic signals arising from planetary interiors. Focusing on an axisymmetric quasi-geostrophic magnetohydrodynamic (MHD) wave -called torsional Alfv\'{e}n waves (TW) – we examine the utility of DMD in two types of MHD direct numerical simulations: Boussinesq magnetoconvection and anelastic convection-driven dynamos in rapidly rotating spherical shells, which model the dynamics in Earth’s core and in Jupiter, respectively. We demonstrate that DMD is capable of distinguishing internal modes and boundary/interface-related modes from the timeseries of the internal velocity. Those internal modes may be realised as free TW, in terms of eigenvalues and eigenfunctions of their normal mode solutions. Meanwhile it turns out that, in order to account for the details, the global TW eigenvalue problems in spherical shells need to be further addressed.

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K. Hori, S. Tobias and R. Teed
Tue, 29 Sep 20
91/98

Comments: 7 pages, 11 figures, Proceedings of the Japan Society of Fluid Mechanics Annual Meeting 2020, Virtual, 18-20 September 2020

Magnetic winding: what is it and what is it good for? [CL]

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http://arxiv.org/abs/2009.11708


Magnetic winding is a fundamental topological quantity that underpins magnetic helicity and measures the entanglement of magnetic field lines. Like magnetic helicity, magnetic winding is also an invariant of ideal magnetohydrodynamics. In this article we give a detailed description of what magnetic winding describes, how to calculate it and how to interpret it in relation to helicity. We show how magnetic winding provides a clear topological description of magnetic fields (open or closed) and we give examples to show how magnetic winding and helicity can behave differently, thus revealing different and imporant information about the underlying magnetic field.

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C. Prior and D. MacTaggart
Fri, 25 Sep 20
-1803/62

Comments: accepted for Proc. R. Soc. A

A model of rotating convection in stellar and planetary interiors: II — gravito-inertial wave generation [SSA]

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http://arxiv.org/abs/2009.10473


Gravito-inertial waves are excited at the interface of convective and radiative regions and by the Reynolds stresses in the bulk of the convection zones of rotating stars and planets. Such waves have notable asteroseismic signatures in the frequency spectra of rotating stars, particularly among rapidly rotating early-type stars, which provides a means of probing their internal structure and dynamics. They can also transport angular momentum, chemical species, and energy from the excitation region to where they dissipate in radiative regions. To estimate the excitation and convective parameter dependence of the amplitude of those waves, a monomodal model for stellar and planetary convection as described in Paper I is employed, which provides the magnitude of the rms convective velocity as a function of rotation rate. With this convection model, two channels for wave driving are considered: excitation at a boundary between convectively stable and unstable regions and excitation due to Reynolds-stresses. Parameter regimes are found where the sub-inertial waves may carry a significant energy flux, depending upon the convective Rossby number, the interface stiffness, and the wave frequency. The super-inertial waves can also be enhanced, but only for convective Rossby numbers near unity. Interfacially excited waves have a peak energy flux near the lower cutoff frequency when the convective Rossby number of the flows that excite them are below a critical Rossby number that depends upon the stiffness of the interface, whereas that flux decreases when the convective Rossby number is larger than this critical Rossby number.

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K. Augustson, S. Mathis and A. Astoul
Wed, 23 Sep 20
-1763/86

Comments: 18 pages, 6 figures, accepted in ApJ

Connections between Non-Rotating, Slowly Rotating, and Rapidly Rotating Turbulent Convection Transport Scalings [CL]

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http://arxiv.org/abs/2009.03447


Buoyancy-driven convection is likely the dominant driver of turbulent motions in the universe, and thus, is widely studied by physicists, engineers, geophysicists and astrophysicists. Maybe unsurprisingly, these different communities discuss the gross convective behaviors in different ways, often without significant cross-talk existing between them. Here, we seek to draw connections between these communities. We do so by carrying out a set of basic scale estimations for how heat and fluid momentum transport should behave in non-rotating, slowly rotating and rapidly rotating buoyancy-driven convective environments. We find that slowly and rapidly rotating scalings can be inter-related via one parameter, the so-called convective Rossby number $\RoC$, a dissipation-free parameter measuring the importance of buoyancy driving relative to rotation. Further, we map between non-flux-based and the flux-based, buoyancy-driven scalings used by different groups. In doing so, these scalings show that there are clean connections between the different communities’ approaches and that a number of the seemingly different scalings are actually synonymous with one another.

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J. Aurnou, S. Horn and K. Julien
Wed, 9 Sep 20
-1457/78

Comments: 15 pages, 3 figures, 2 Tables

On the evolution of global ocean tides [EPA]

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http://arxiv.org/abs/2009.00204


We apply Laplace’s tidal theory to the evolution of lunar and solar tides on the geologic timescale of Earth’s rotation and focus on the tidal resonance. We study the global tide in the mid-ocean far away from continents. On the short timescale, a linear relationship of tidal height and Earth’s rotation is obtained. On the long timescale, the tide is less than 1 metre at present but it was 5 metres in the past and will reach 8 metres in the future because of resonances of tidal wave and Earth’s rotation. We conclude that the Earth-Moon orbital separation and the slowdown of Earth’s rotation are faster than expected before.

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X. Wei
Wed, 2 Sep 20
-1329/65

Comments: N/A

Effects of Solar Activity on Taylor Scale and Correlation Scale in Solar Wind Magnetic Fluctuations [CL]

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http://arxiv.org/abs/2008.08542


The correlation scale and the Taylor scale are evaluated for interplanetary magnetic field fluctuations from two-point, single time correlation function using the Advanced Composition Explorer (ACE), Wind, and Cluster spacecraft data during the time period from 2001 to 2017, which covers over an entire solar cycle. The correlation scale and the Taylor scale are respectively compared with the sunspot number to investigate the effects of solar activity on the structure of the plasma turbulence. Our studies show that the Taylor scale increases with the increasing sunspot number, which indicates that the Taylor scale is positively correlated with the energy cascade rate, and the correlation coefficient between the sunspot number and the Taylor scale is 0.92. However, these results are not consistent with the traditional knowledge in hydrodynamic dissipation theories. One possible explanation is that in the solar wind, the fluid approximation fails at the spatial scales near the dissipation ranges. Therefore, the traditional hydrodynamic turbulence theory is incomplete for describing the physical nature of the solar wind turbulence, especially at the spatial scales near the kinetic dissipation scales.

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G. Zhou, H. He and W. Wan
Thu, 20 Aug 20
-1092/48

Comments: Published in ApJL

SN Ia DDT Explosions Powered by the Zeldovich Reactivity Gradient Mechanism [SSA]

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http://arxiv.org/abs/2008.05010


The aim of this work is to identify and explain the necessary conditions required for an energetic explosion of a Chandrasekhar-mass white dwarf. We construct and analyze weakly compressible turbulence models with nuclear burning effects for carbon/oxygen plasma at a density expected for deflagration-to-detonation transition (DDT) to occur. We observe formation of carbon deflagrations and transient carbon detonations at early times. As turbulence becomes increasingly inhomogeneous, sustained carbon detonations are initiated by the Zel’dovich reactivity gradient mechanism. The fuel is suitably preconditioned by the action of compressive turbulent modes with wavelength comparable to the size of resolved turbulent eddies; no acoustic wave is involved in this process. Oxygen detonations are initiated either aided by reactivity gradients or by collisions of carbon detonations. The observed evolutionary timescales are found sufficiently short for the above process to occur in the expanding, centrally ignited massive white dwarf. The inhomogeneous conditions produced prior to DDT might be of consequence for the chemical composition of the outer ejecta regions of SN Ia from the single degenerate channel, and offer potential for validation of the proposed model.

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E. Brooker, T. Plewa and D. Fenn
Thu, 13 Aug 20
-917/67

Comments: 5 pages, 4 figures, MNRAS in press

Single-hemisphere dynamos in M-dwarf stars [SSA]

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http://arxiv.org/abs/2008.02362


M-dwarf stars below a certain mass are convective from their cores to their photospheres. These fully convective objects are extremely numerous, very magnetically active, and the likely hosts of many exoplanets. Here we study, for the first time, dynamo action in simulations of stratified, rotating fully convective M-dwarf stars. Importantly, we use new techniques to capture the correct full ball geometry down to the center of the star. We find surprising dynamo states in these systems, with the global-scale mean fields confined strongly to a single hemisphere, in contrast to prior stellar dynamo solutions. These hemispheric-dynamo stars are likely to have profoundly different interactions with their surroundings, with important implications for exoplanet habitability and stellar spindown.

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B. Brown, J. Oishi, G. Vasil, et. al.
Fri, 7 Aug 20
-749/46

Comments: 7 pages, 3 figures; submitted to ApJL

Magnetohydrodynamics of protoplanetary discs [SSA]

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http://arxiv.org/abs/2007.15967


Protoplanetary discs are made of gas and dust orbiting a young star. They are also the birth place of planetary systems, which motivates a large amount of observational and theoretical research.
In these lecture notes, I present a review of the magnetic mechanisms applied to the outer regions R>1 AU of these discs, which are the planet-formation regions. In contrast to usual astrophysical plasmas, the gas in these regions is noticeably cold (T<300 K) and dense, which implies a very low ionisation fraction close to the disc midplane. In these notes, I deliberately ignore the innermost R~0.1 AU region which is influenced by the star-disk interaction and various radiative effects.
I start by presenting a short overview of the observational evidence for the dynamics of these objects. I then introduce the methods and approximations used to model these plasmas, including non-ideal MHD, and the uncertainties associated with this approach. In this framework, I explain how the global dynamics of these discs is modelled, and I present a stability analysis of this plasma in the local approximation, introducing the non-ideal magneto-rotational instability. Following this mostly analytical part, I discuss numerical models which have been used to describe the saturation mechanisms of this instability, and the formation of large-scale structures by various saturation mechanisms. Finally, I show that local numerical models are insufficient since magnetised winds are also emitted from the surface of these objects. After a short introduction on winds physics, I present global models of protoplanetary discs, including both a large-scale wind and the non-ideal dynamics of the disc.

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G. Lesur
Mon, 3 Aug 20
-654/58

Comments: 115 pages, 46 figures, accepted for publication in the lecture notes series of the Journal of Plasma Physics (Cambridge University Press)

Estimating the energy dissipation {from Kelvin-Helmholtz instability induced} turbulence in oscillating coronal loops} [SSA]

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http://arxiv.org/abs/2007.09068


Kelvin-Helmholtz {instability induced} turbulence is one promising mechanism by which loops in the solar corona can be heated by MHD waves. In this paper we present an analytical model of the dissipation rate of {Kelvin-Helmholtz instability induced} turbulence $\varepsilon_{\rm D}$, finding it scales as the wave amplitude ($d$) to the third power ($\varepsilon_{\rm D}\propto d^3$). Based on the concept of steady-state turbulence, we expect the turbulence heating throughout the volume of {the} loop to match the total energy injected through its footpoints. In situations where this holds, the wave amplitude has to vary as the cube-root of the injected energy. Comparing the analytic results with those of simulations shows that our analytic formulation captures the key aspects of the turbulent dissipation from the numerical work. Applying this model to the observed characteristics of decayless kink waves we predict that the amplitudes of these observed waves is insufficient to turbulently heat the solar corona.

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A. Hillier, T. Doorsselaere and K. Karampelas
Mon, 20 Jul 20
-341/85

Comments: 6 pages, 1 figure, published in ApJL

Deep rotating convection generates the polar hexagon on Saturn [CL]

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http://arxiv.org/abs/2007.08958


Numerous land and space-based observations have established that Saturn has a persistent hexagonal flow pattern near its north pole. While observations abound, the physics behind its formation is still uncertain. Although several phenomenological models have been able to reproduce this feature, a self-consistent model for how such a large-scale polygonal jet forms in the highly turbulent atmosphere of Saturn is lacking. Here we present a 3D fully-nonlinear anelastic simulation of deep thermal convection in the outer layers of gas giant planets which spontaneously generates giant polar cyclones, fierce alternating zonal flows, and a high latitude eastward jet with a polygonal pattern. The analysis of the simulation suggests that self-organized turbulence in the form of giant vortices pinches the eastward jet, forming polygonal shapes. We argue that a similar mechanism is responsible for exciting Saturn’s hexagonal flow pattern.

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R. Yadav and J. Bloxham
Mon, 20 Jul 20
-305/85

Comments: 11 pages, 4 main and 5 supplementary figures, 1 animation, 42 references

Observational quantification of three-dimensional anisotropies and scalings of space plasma turbulence at kinetic scales [CL]

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http://arxiv.org/abs/2006.02722


A statistical survey of spectral anisotropy of space plasma turbulence is performed using five years measurements from MMS in the magnetosheath. By measuring the five-point second-order structure functions of the magnetic field, we have for the first time quantified the three-dimensional anisotropies and scalings at sub-ion-scales ($<$ 100 km). In the local reference frame $(\hat L_{\perp}, \hat l_{\perp}, \hat l_{\parallel})$ defined with respect to local mean magnetic field $\boldsymbol {B}0$ (Chen et al. 2012), the “statistical eddies” are found to be mostly elongated along $\boldsymbol {B}_0$ and shortened in the direction perpendicular to both $\boldsymbol {B}_0$ and local field fluctuations. From several $d_i$ (ion inertial length) toward $\sim$ 0.05 $d_i$, the ratio between eddies’ parallel and perpendicular lengths features a trend of rise then fall, whereas the anisotropy in the perpendicular plane appears scale-invariant. Specifically, the anisotropy relations for the total magnetic field at 0.1-1.0 $d_i$ are obtained as $l{\parallel} \simeq 2.44 \cdot l_{\perp}^{0.71}$, and $L_{\perp} \simeq 1.58 \cdot l_{\perp}^{1.08}$, respectively. Our results provide new observational evidence to compare with phenomenological models and numerical simulations, which may help to better understand the nature of kinetic scale turbulence.

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T. Wang, J. He, O. Alexandrova, et. al.
Fri, 5 Jun 20
57/70

Comments: Accepted

Noether Currents for Eulerian Variational Principles in Non Barotropic Magnetohydrodynamics and Topological Conservations Laws [CL]

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http://arxiv.org/abs/2005.14005


We derive a Noether current for the Eulerian variational principle of ideal non-barotropic magnetohydrodynamics (MHD). It was shown previously that ideal non-barotropic MHD is mathematically equivalent to a five function field theory with an induced geometrical structure in the case that field lines cover surfaces and this theory can be described using a variational principle. Here we use various symmetries of the flow to derive topological constants of motion through the derived Noether current and discuss their implication for non-barotropic MHD.

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A. Yahalom and H. Qin
Fri, 29 May 20
62/75

Comments: 34 pages. arXiv admin note: substantial text overlap with arXiv:1510.00637, arXiv:1703.08072, arXiv:1801.06443, arXiv:physics/0603115

Rotating self-gravitating Bose-Einstein condensates with a crust: a minimal model for pulsar glitches [HEAP]

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http://arxiv.org/abs/2005.13310


We develop a minimal model for \textit{pulsar glitches} by introducing a solid-crust potential in the three-dimensional (3D) Gross-Pitaevskii-Poisson equation (GPPE), which we have used earlier to study gravitationally bound Bose-Einstein Condensates (BECs), i.e., bosonic stars. In the absence of the crust potential, we show that, if we rotate such a bosonic star, it is threaded by vortices. We then show, via extensive direct numerical simulations (DNSs), that the interaction of these vortices with the crust potential yields (a) stick-slip dynamics and (b) dynamical glitches. We demonstrate that, if enough momentum is transferred to the crust from the bosonic star, then the vortices are expelled from the star and the crust’s angular momentum $J_c$ exhibits features that can be interpreted naturally as glitches. From the time series of $J_c$, we compute the cumulative probability distribution functions (CPDFs) of event sizes, event durations, and waiting times. We show that these CPDFs have signatures of self-organized criticality (SOC), which have been seen in observations on pulsar glitches.

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A. Verma, R. Pandit and M. Brachet
Thu, 28 May 20
14/55

Comments: N/A

Deceleration of relativistic jets with lateral expansion [HEAP]

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http://arxiv.org/abs/2005.10313


We present a model for the hydrodynamics of a relativistic jet interacting with the circum-stellar medium (CSM). The shocked CSM and the jet material are assumed to be in an infinitely thin surface, so the original 2D problem is effectively reduced to 1D. From general conservation laws, we derive the equation of motion for each fluid element along this surface, taking into account the deceleration along the surface normal due to newly swept-up mass and lateral expansion due to pressure gradient in the tangential direction. The pressure and energy density of the shocked CSM are given by the jump conditions at the forward shock. The method is implemented with a finite-differencing numerical scheme, along with calculation of synchrotron emission and absorption from shock-accelerated electrons, in a new code $\mathtt{Jedi}$ (for “jet dynamics”). We present a number of test cases, including top-hat jet, power-law structured jet, “boosted fireball” profile, and CSM with density jump at the wind termination shock. Based on the agreement with other analytical and numerical calculations, we conclude that our simplified method provides a good approximation for the hydrodynamics and afterglow emission for a wide variety of jet structures and CSM density profiles. Efficient modeling of the afterglow from e.g., neutron star mergers, will provide important information on the jet energetics, CSM properties, and the viewing angle.

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W. Lu, P. Beniamini and A. McDowell
Fri, 22 May 20
34/64

Comments: 12 pages, 12 figures, plus appendices. Comments welcome!

A Detailed Examination of Anisotropy and Timescales inThree-dimensional Incompressible Magnetohydrodynamic Turbulence [CL]

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http://arxiv.org/abs/2005.08815


When magnetohydrodynamic turbulence evolves in the presence of a large-scale mean magnetic field, an anisotropy develops relative to that preferred direction. The well-known tendency is to develop stronger gradients perpendicular to the magnetic field, relative to the direction along the field. This anisotropy of the spectrum is deeply connected with anisotropy of estimated timescales for dynamical processes, and requires reconsideration of basic issues such as scale locality and spectral transfer. Here analysis of high-resolution three-dimensional simulations of unforced magnetohydrodynamic turbulence permits quantitative assessment of the behavior of theoretically relevant timescales in Fourier wavevector space. We discuss the distribution of nonlinear times, Alfv\’en times, and estimated spectral transfer rates. Attention is called to the potential significance of special regions of the spectrum, such as the two-dimensional limit and the “critical balance” region. A formulation of estimated spectral transfer in terms of a suppression factor supports a conclusion that the quasi two-dimensional fluctuations (characterized by strong nonlinearities) are not a singular limit, but may be in general expected to make important contributions.

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R. Chhiber, W. Matthaeus, S. Oughton, et. al.
Tue, 19 May 20
35/92

Comments: In Press at Physics of Plasmas

Libration-driven inertial waves and mean zonal flows in spherical shells [CL]

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http://arxiv.org/abs/2005.06345


Several planetary bodies in our solar system undergo a forced libration owing to gravitational interactions with their orbital companions, leading to complex fluid motions in their metallic liquid cores or subsurface oceans. In this study, we numerically investigate flows in longitudinally librating spherical shells. We focus on the Ekman number dependencies of several shear layers when the libration frequency is less than twice of the rotation frequency and the libration amplitude is small. Time-dependent flows mainly consist of inertial waves excited at the critical latitudes due to the Ekman pumping singularities, forming conical shear layers. In particular, previous theoretical studies have proposed different scalings for the conical shear layers spawned from the critical latitudes at the inner boundary. Our numerical results favor the velocity amplitude scaling $\mathrm{O}(\varepsilon E^{1/12})$ predicted by Le Diz`es \& Le Bars (2017) over the scaling $\mathrm{O}(\varepsilon E^{1/6})$ initially proposed by Kerswell (1995), though the Ekman numbers in our calculations are not sufficiently small to pin down this scaling. Non-linear interactions in the boundary layers drive a mean zonal flow with several geostrophic shears. Our numerical results show that geostrophic shears associated with the critical latitudes at the inner and outer boundaries exhibit the same scalings, i.e. an amplitude of $\mathrm{O}(\varepsilon^2 E^{-1/10})$ over a width of $\mathrm{O}(E^{1/5})$. Apart from the geostrophic shear associated with the critical latitude, our numerical results show that the reflection of inertial waves can induce a geostrophic shear with an amplitude of $\mathrm{O}(\varepsilon^2 E^{-1/6})$ over a width of $\mathrm{O}(E^{1/3})$.

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Y. Lin and J. Noir
Thu, 14 May 20
6/56

Comments: 20 pages, 18 figures; published in GAFD

A new class of discontinuous solar wind solutions [SSA]

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http://arxiv.org/abs/2005.06426


A new class of one-dimensional solar wind models is developed within the general polytropic, single-fluid hydrodynamic framework. The particular case of quasi-adiabatic radial expansion with a localized heating source is considered. We consider analytical solutions with continuous Mach number over the entire radial domain while allowing for jumps in the flow velocity, density, and temperature, provided that there exists an external source of energy in the vicinity of the critical point which supports such jumps in physical quantities. This is substantially distinct from both the standard Parker solar wind model and the original nozzle solutions, where such discontinuous solutions are not permissible. We obtain novel sample analytic solutions of the governing equations corresponding to both slow and fast wind.

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B. Shergelashvili, V. Melnik, G. Dididze, et. al.
Thu, 14 May 20
18/56

Comments: 13 pages, 3 figures, MNRAS, Accepted for publication

Angular momentum transport, layering, and zonal jet formation by the GSF instability: nonlinear simulations at a general latitude [SSA]

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http://arxiv.org/abs/2005.04941


We continue our investigation into the nonlinear evolution of the Goldreich-Schubert-Fricke (GSF) instability in differentially rotating radiation zones. This instability may be a key player in transporting angular momentum in stars and giant planets, but its nonlinear evolution remains mostly unexplored. In a previous paper we considered the equatorial instability, whereas here we simulate the instability at a general latitude for the first time. We adopt a local Cartesian Boussinesq model in a modified shearing box for most of our simulations, but we also perform some simulations with stress-free, impenetrable, radial boundaries. We first revisit the linear instability and derive some new results, before studying its nonlinear evolution. The instability is found to behave very differently compared with its behaviour at the equator. In particular, here we observe the development of strong zonal jets (“layering” in the angular momentum), which can considerably enhance angular momentum transport, particularly in axisymmetric simulations. The jets are, in general, tilted with respect to the local gravity by an angle that corresponds initially with that of the linear modes, but which evolves with time and depends on the strength of the flow. The instability transports angular momentum much more efficiently (by several orders of magnitude) than it does at the equator, and we estimate that the GSF instability could contribute to the missing angular momentum transport required in both red giant and subgiant stars. It could also play a role in the long-term evolution of the solar tachocline and the atmospheric dynamics of hot Jupiters.

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A. Barker, C. Jones and S. Tobias
Tue, 12 May 20
40/64

Comments: Accepted for publication in MNRAS on 8th May 2020

The structure of nearly isothermal, adiabatic shockwaves [HEAP]

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http://arxiv.org/abs/2005.03707


An explosively generated shockwave with time-dependent radius $R(t)$ is characterized by a phase in which the shocked gas becomes radiative with an effective adiabatic index $\gamma \simeq 1$. Using the result that the post-shock gas is compressed into a shell of width $\Delta R/R \simeq \delta$, where $\delta = \gamma-1$, we show that a choice of self-similar variable that exploits this compressive behavior in the limit that $\gamma \rightarrow 1$ naturally leads to a series expansion of the post-shock fluid density, pressure, and velocity in the small quantity $\delta$. We demonstrate that the leading-order (in $\delta$) solutions, which are increasingly accurate as $\gamma \rightarrow 1$, can be written in simple, closed forms when the fluid is still approximated to be in the energy-conserving regime (i.e., the Sedov-Taylor limit), and that the density declines exponentially rapidly with distance behind the shock. We also analyze the solutions for the bubble surrounding a stellar or galactic wind that interacts with its surroundings, and derive expressions for the location of the contact discontinuity that separates the shocked ambient gas from the shocked wind. We discuss the implications of our findings in the context of the dynamical stability of nearly isothermal shocks.

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E. Coughlin
Mon, 11 May 20
44/61

Comments: 5 pages, 2 figures, MNRASL Accepted

A global model of the magnetorotational instability in protoneutron stars [HEAP]

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http://arxiv.org/abs/2005.03567


Magnetars are highly magnetized neutron stars whose magnetic dipole ranges from $10^{14}$ to $10^{15}$ G. The MRI is considered to be a promising mechanism to amplify the magnetic field in fast-rotating protoneutron stars and form magnetars. This scenario is supported by many local studies showing that magnetic fields could be amplified by the MRI on small scales. However, the efficiency of the MRI at generating a dipole field is still unknown. To answer this question, we study the MRI dynamo in an idealized global model of a fast rotating protoneutron star with differential rotation. We perform 3D incompressible MHD simulations in spherical geometry with explicit diffusivities where the differential rotation is forced at the outer boundary. We vary the initial magnetic field and investigated different magnetic boundary conditions. These simulations were compared to local shearing box simulations. We obtain a self-sustained turbulent MRI-driven dynamo, whose saturated state is independent of the initial magnetic field. The MRI generates a strong turbulent magnetic field of $B \geq 2\times 10^{15}$ G and a non-dominant magnetic dipole, which represents systematically about $5\%$ of the averaged magnetic field strength. Interestingly, this dipole is tilted towards the equatorial plane. We find that local shearing box models can reproduce fairly well several characteristics of global MRI turbulence such as the kinetic and magnetic spectra. The turbulence is nonetheless more vigorous in the local models than in the global ones. Overall, our results support the ability of the MRI to form magnetar-like large-scale magnetic fields. They furthermore predict the presence of a stronger small-scale magnetic field. The resulting magnetic field could be important to power outstanding stellar explosions, such as superluminous supernovae and GRBs.

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A. Reboul-Salze, J. Guilet, R. Raynaud, et. al.
Fri, 8 May 20
63/72

Comments: Submitted to A&A, 15 pages, 21 figures

A study of daytime convective vortices and turbulence in the martian Planetary Boundary Layer based on half-a-year of InSight atmospheric measurements and Large-Eddy Simulations [EPA]

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http://arxiv.org/abs/2005.01134


Studying the atmospheric Planetary Boundary Layer (PBL) is crucial to understand the climate of a planet. The meteorological measurements by the instruments onboard InSight make a uniquely rich dataset to study the active turbulent dynamics of the daytime PBL on Mars. Here we use the high-sensitivity continuous pressure, wind, temperature measurements in the first 400 sols of InSight operations to analyze convective gusts, cells, and vortices in Mars’ daytime PBL. We compare the InSight measurements to turbulence-resolving Large-Eddy Simulations (LES). The daytime PBL turbulence at the InSight landing site is found to be very active, with clearly identified signatures of convective cells and a vast population of almost 10,000 recorded vortex encounters, adequately represented by a power-law with a 3.5 exponent in agreement with LES results. While the daily variability of vortex encounters at the InSight landing site can be explained by the statistical nature of turbulence, the seasonal variability is strongly correlated with ambient wind speed, which is supported by LES. However, wind gustiness is more correlated to surface temperature than ambient wind speed, confirming the radiative control of the daytime martian PBL; and fewer convective vortices are forming in LES when the background wind is doubled. Thus, the long-term seasonal variability of vortex encounters at the InSight landing site is mainly controlled by the advection of convective vortices by the ambient wind speed. Typical tracks followed by vortices forming in the LES show a similar distribution in direction and length as orbital imagery of the InSight region.

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A. Spiga, N. Murdoch, R. Lorenz, et. al.
Tue, 5 May 20
56/75

Comments: 39 pages, 16 figures, manuscript not yet peer-reviewed and submitted to Journal of Geophysical Research Planets (InSight special issue)

Anelastic equatorial waves with the complete Coriolis terms [CL]

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http://arxiv.org/abs/2004.15017


This study derives a complete set of equatorially confined wave solutions from an anelastic equation set with the complete Coriolis terms, which include both the vertical and meridional planetary vorticity. The propagation mechanism can change with the effective static stability. When the effective static stability reduces to neutral, buoyancy ceases, but the role of buoyancy as an eastward-propagation mechanism is replaced by the compressional beta-effect, i.e., vertical density-weighted advection of the meridional planetary vorticity. For example, the Kelvin mode becomes a compressional Rossby mode. Compressional Rossby waves are meridional vorticity disturbances that propagate eastward owing to the compressional beta-effect. The compressional Rossby wave solutions can serve as a benchmark to validate the implementation of the nontraditional Coriolis terms (NCTs); with an effectively neutral condition and initial large-scale disturbances given a half vertical wavelength spanning the troposphere on Earth, compressional Rossby waves are expected to propagate eastward at a phase speed of 0.24 m s${}^{-1}$. The phase speed increases with the planetary rotation rate and the vertical wavelength and also changes with the density scale height. Besides, the compressional beta-effect and the meridional vorticity tendency are reconstructed using reanalysis data and regressed upon tropical precipitation filtered for the Madden$-$Julian oscillation (MJO). The results suggest that the compressional beta-effect contributes 10.8% of the meridional vorticity budget associated with the MJO in terms of the ratio of the minimum values. The complete set of statically neutral equatorial waves may be significant in the interiors of stars and giant planets.

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H. Ong and P. Roundy
Mon, 4 May 20
10/55

Comments: 18 pages, 3 figures, submitted to J. Atmos. Sci. This paper originated as a course project of Hing Ong in ATM 523, Large Scale Dynamics of the Tropics, instructed by Paul Roundy. It became a chapter of Hing Ong’s PhD dissertation

On the Origin of Optical Radiation during the Impulsive Phase of Flares on dMe Stars. I. Discussion of Gas Dynamic Models [SSA]

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http://arxiv.org/abs/2004.14508


In connection with a published critique, the author justifies the use of a motionless homogeneous plane layer of pure hydrogen plasma that is near local thermodynamic equilibrium (LTE) for analyzing the characteristics of the radiation from a chromospheric condensation of thickness $\Delta{}z_m=10\text{ km}$ in a gas dynamic model of stellar flares. It is shown that the shock-wave model of flares proposed by Belova and Bychkov, as opposed to the model of Kostyuk and Pikelner, has irremovable internal defects owing to exclusion of the interaction between a thermal wave (temperature jump) and a non-stationary radiative shock. In particular, this model (a) does not make it possible to increase the geometric thickness of a chromospheric condensation owing to divergence of the fronts of the thermal and shock waves during impulsive heating, (b) cannot provide heating of the chromospheres of red dwarfs over significant distances, and (c) predicts $\mathrm{H}_\alpha$ line profiles in conflict with observational data. It is argued that: (a) the shock-wave model by Belova and Bychkov represents a development of the kinematic model of solar flares (Nakagawa et al.) and its application to dMe stars, specifically: a study of the radiative response of the chromosphere of a red dwarf to impulsive heating in the simplest gas dynamic statement of the problem (a thermal wave is excluded, a stationary approach is used); (b) in terms of the Kostyuk and Pikelner model, the regions behind the stationary shock fronts do not correspond to a chromospheric condensation with time-varying thickness but to zones in which the plasma relaxes to a state of thermal equilibrium. It is emphasized that the separation of the Kostyuk and Pikelner model into “thermal” and “shock-wave” components is fundamentally impossible.

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E. Morchenko
Fri, 1 May 20
49/54

Comments: 17 pages, 1 figure, published in Astrophysics. Keywords: red dwarf stars: flares: impulsive heating: gas dynamic models: optical radiation

Dynamical friction with radiative feedback — II. High resolution study of the subsonic regime [EPA]

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http://arxiv.org/abs/2004.13422


Recent work has suggested that the net gravitational force acting on a massive and luminous perturber travelling through a gaseous and opaque medium can have same direction as the perturber’s motion (an effect sometimes called negative dynamical friction). Analytic results were obtained using a linear analysis and were later confirmed by means of non-linear numerical simulations which did not resolve the flow within the Bondi sphere of the perturber, hence effectively restricted to weakly perturbed regions of the flow (paper~I). Here we present high resolution simulations, using either 3D Cartesian or 2D cylindrical meshes that resolve the flow within the Bondi sphere. We perform a systematic study of the force as a function of the perturber’s mass and luminosity, in the subsonic regime. We find that perturbers with mass $M$ smaller than a few $M_c\sim \chi c_s/G$ are subjected to a thermal force with a magnitude in good agreement with linear theory ($\chi$ being the thermal diffusivity of the medium, $c_s$ the adiabatic sound speed and $G$ the gravitational constant), while for larger masses, the thermal forces are only a fraction of the linear estimate that decays as $M^{-1}$. Our analysis confirms the possibility of negative friction (hence a propulsion) on sufficiently luminous, low-mass embryos embedded in protoplanetary discs. Finally, we give an approximate expression of the total force at low Mach number, valid both for sub-critical ($M<M_c$) and super-critical ($M>M_c$) perturbers.

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D. Velasco-Romero and F. Masset
Wed, 29 Apr 20
45/75

Comments: N/A