Horizontal shear instabilities in rotating stellar radiation zones

Abstract

Context. Stellar interiors are the seat of efficient transport of angular momentum all along their evolution. In this context, understanding the dependence of the turbulent transport triggered by the instabilities of the vertical and horizontal shears of the differential rotation in stellar radiation zones as a function of their rotation, stratification, and thermal diffusivity is mandatory. Indeed, it constitutes one of the cornerstones of the rotational transport and mixing theory, which is implemented in stellar evolution codes to predict the rotational and chemical evolutions of stars. Aims. We investigate horizontal shear instabilities in rotating stellar radiation zones by considering the full Coriolis acceleration with both the dimensionless horizontal Coriolis component f̃ and the vertical component f. Methods. We performed a linear stability analysis using linearized equations derived from the Navier-Stokes and heat transport equations in the rotating nontraditional f-plane. We considered a horizontal shear flow with a hyperbolic tangent profile as the base flow. The linear stability was analyzed numerically in wide ranges of parameters, and we performed an asymptotic analysis for large vertical wavenumbers using the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) approximation for nondiffusive and highly-diffusive fluids. Results. As in the traditional f-plane approximation, we identify two types of instabilities: the inflectional and inertial instabilities. The inflectional instability is destabilized as f̃ increases and its maximum growth rate increases significantly, while the thermal diffusivity stabilizes the inflectional instability similarly to the traditional case. The inertial instability is also strongly affected; for instance, the inertially unstable regime is also extended in the nondiffusive limit as 0 < f < 1 + f̃ 2/N2, where N is the dimensionless Brunt-Väisälä frequency. More strikingly, in the high thermal diffusivity limit, it is always inertially unstable at any colatitude θ except at the poles (i.e., 0° < θ < 180°). We also derived the critical Reynolds numbers for the inertial instability using the asymptotic dispersion relations obtained from the WKBJ analysis. Using the asymptotic and numerical results, we propose a prescription for the effective turbulent viscosities induced by the inertial and inflectional instabilities that can be possibly used in stellar evolution models. The characteristic time of this turbulence is short enough so that it is efficient to redistribute angular momentum and to mix chemicals in stellar radiation zones.

Anisotropic turbulent transport with horizontal shear in stellar radiative zones

“…In the case where the dynamics is dominated by the horizontal shear, assuming τ ∼ 1/S θ further leads to a horizontal viscosity coefficient that is proportional to the horizontal shear rate, which is consistent with the viscosity coefficient derived by Park et al (2021). We note that, in contrast, Garaud (2001) found that the horizontal shear instability can lead to an anti-diffusive horizontal transport of angular momentum.…”

“…Besides, the comparison with the Rayleigh-Taylor instability stands only in the special case where 2Ω + sin θS r > 0 and cos S θ < 0. Thus, the criterion |S θ | < 2 could be linked to some other hydrodynamical instability instead, such as the inertial or the inflectional instability studied by Park et al (2020Park et al ( , 2021. The form of the expression of u θ u ϕ in Eq.…”

“…For a complete treatment of thermal diffusion, we refer the reader to Park et al (2020Park et al ( , 2021. These two equations can be combined into a single one by expressing entropy fluctuations as a function of density fluctuations:…”

“…The first numerical simulations of the turbulent transport triggered by the instabilities of a horizontal shear in stellar conditions have also been performed (Cope et al 2020;Garaud 2020). Finally, Park et al (2020Park et al ( , 2021 studied the linear instabilities of the horizontal differential rotation in stellar radiation zones as a function of stratification, rotation, and thermal diffusivity.…”

The complex interplay between tidal inertial waves and zonal flows in differentially rotating stellar and planetary convective regions

“…Guenel et al (2016a,b) did observe instabilities with conical differential rotation, but only for sufficiently low viscosities, whereas our study shows little dependence on the friction and rather highlights possible over-transmission for non-linear flows. Lastly, we underline that a temporal analysis on the growth rate of perturbations should be undertaken to unravel instabilities, which has not been performed in this paper but has been in other separate papers (Park et al 2020(Park et al , 2021.…”