http://arxiv.org/abs/1910.09860
The so-called rotational mixing, which transports angular momentum and chemical elements in stellar radiative zones, is one of the key processes for modern stellar evolution. In the two last decades, the stress has been put on the turbulent transport induced by the vertical shear instability. However, the instabilities of horizontal shears and the strength of the anisotropic turbulent transport they may trigger are still largely unknown. In this paper, we investigate the combined effects of stable stratification, rotation, and thermal diffusion on the instabilities of horizontal shears in the context of stellar radiative zones. The eigenvalue problem describing the instabilities of a flow with a hyperbolic-tangent horizontal shear profile is solved numerically and asymptotically by means of the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) analysis to provide explicit asymptotic dispersion relations in non-diffusive and highly diffusive limits. Two types of instabilities are identified: the inflectional and the inertial instabilities. The inflectional instability is most unstable at finite streamwise wavenumber and zero vertical wavenumber, independently of the stratification, rotation, and thermal diffusion. It is favored by stable stratification but stabilized by thermal diffusion. The inertial instability is driven by rotation and the WKBJ analysis reveals that the growth rate reaches its maximum in the inviscid limit: $\sqrt{f(1-f)}$ (where $f$ is the dimensionless Coriolis parameter). The inertial instability for finite vertical wavenumber is stabilized as the stratification increases for non-diffusive fluids, while it becomes independent of the stratification and stronger for fluids with high thermal diffusivity. Furthermore, we found a self-similarity of the instabilities based on the rescaled parameter $PeN^{2}$ with the P\’eclet number $Pe$ and the Brunt-V\”ais\”al\”a frequency $N$.
J. Park, V. Prat and S. Mathis
Wed, 23 Oct 19
30/64
Comments: Submitted to A&A