Modeling coexisting GSF and shear instabilities in rotating stars

Abstract

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

arXiv comment19 pages, 11 figures

References in corpus (21)

• Modules for Experiments in Stellar Astrophysics (MESA)
• Probing the interior physics of stars through asteroseismology
• Numerically determined transport laws for fingering ("thermohaline") convection in astrophysics
• Chemical Transport and Spontaneous Layer Formation in Fingering Convection in Astrophysics
• Dynamics of fingering convection II: The formation of thermohaline staircases
• Turbulent transport in radiative zones of stars
• The effect of Prandtl number on turbulent sheared thermal convection
• Shear mixing in stellar radiative zones - II. Robustness of numerical simulations
• Shear mixing in stellar radiative zones I. Effect of thermal diffusion and chemical stratification
• Turbulent transport by diffusive stratified shear flows: from local to global models. Part I: Numerical simulations of a stratified plane Couette flow
• Enhanced mixing in magnetized fingering convection, and implications for RGB stars
• The dynamics of stratified horizontal shear flows at low Péclet number
• The stability of stratified spatially periodic shear flows at low Péclet number
• The effect of rotation on oscillatory double-diffusive convection (semiconvection)
• Horizontal shear instabilities at low Prandtl number
• Turbulent transport in a strongly stratified forced shear layer with thermal diffusion
• Angular momentum transport by the GSF instability: nonlinear simulations at the equator
• Potential Vorticity Mixing in a Tangled Magnetic Field
• The interaction between shear and fingering (thermohaline) convection
• Turbulent transport by diffusive stratified shear flows: from local to global models. Part II: Limitations of local models
• Angular momentum transport, layering, and zonal jet formation by the GSF instability: nonlinear simulations at a general latitude

Cited by in corpus (5)

• Chemical Mixing Induced by Internal Gravity Waves in Intermediate Mass Stars
• The effects of surface fossil magnetic fields on massive star evolution: IV. Grids of models at Solar, LMC, and SMC metallicities
• Linear and nonlinear properties of the Goldreich-Schubert-Fricke instability in stellar interiors with arbitrary local radial and latitudinal differential rotation
• Centrifugal instability of Taylor-Couette flow in stratified and diffusive fluids
• Understanding hydrodynamical wave-driven shear mixing in stellar radiation zones. Looking in the mirror of the dyapicnal oceanic mixing