Evolution and characteristics of forced shear flows in polytropic atmospheres: Large and small P\'eclet number regimes

TL;DR

This study uses numerical simulations to analyze the dynamics of shear flows in polytropic atmospheres, focusing on how parameters like viscosity and thermal diffusivity influence turbulence and mixing in stellar interiors.

Contribution

It provides the first detailed analysis of the global properties of saturated shear turbulence, including the spread of shear regions, in different Péclet number regimes.

Findings

Vertical extent of mixing correlates with initial Richardson number.

Turbulence characteristics depend on Richardson number and thermal diffusivity.

Saturated flows of secular shear instability are characterized in low Péclet number regimes.

Abstract

Complex mixing and magnetic field generation occurs within stellar interiors particularly where there is a strong shear flow. To obtain a comprehensive understanding of these processes, it is necessary to study the complex dynamics of shear regions. Due to current observational limitations, it is necessary to investigate the inevitable small-scale dynamics via numerical calculations. Here, we examine direct numerical calculations of a local model of unstable shear flows in a compressible polytropic fluid primarily in a two-dimensional domain, where we focus on determining how key parameters affect the global properties and characteristics of the resulting saturated turbulent phase. We consider the effect of varying both the viscosity and the thermal diffusivity on the non-linear evolution. Moreover, our main focus is to understand the global properties of the saturated phase, in particular estimating for the first time the spread of the shear region from an initially hyperbolic tangent velocity profile. We find that the vertical extent of the mixing region in the saturated regime is generally determined by the initial Richardson number of the system. Further, the characteristic quantities of the turbulence, i.e. typical length-scale and the root-mean-square velocity are found to depend on both the Richardson number, and the thermal diffusivity. Finally, we present our findings of our investigation into saturated flows of a `secular' shear instability in the low P\'eclet number regime with large Richardson numbers.