A model of the entropy flux and Reynolds stress in turbulent convection

TL;DR

This paper introduces a closure model for entropy and momentum transport in astrophysical turbulence, applicable to stellar convection zones, unifying heat and angular momentum transport in rotating stars.

Contribution

The paper presents a novel closure model for turbulent convection that extends from Boussinesq to compressible regimes, capturing key angular momentum and heat flux behaviors in stars.

Findings

Model recovers the Lambda-effect in slow rotation

Predicted heat flux matches mixing-length theory in spherical symmetry

Provides a unified framework for heat and angular momentum transport

Abstract

We propose a closure model for the transport of entropy and momentum in astrophysical turbulence, intended for application to rotating stellar convective regions. Our closure model is first presented in the Boussinesq formalism, and compared with laboratory and numerical experimental results on Rayleigh-Benard convection and Homogeneous Rayleigh-Benard convection. The predicted angular momentum transport properties of the turbulence in the slowly rotating case recover the well-known Lambda-effect, with an amplitude uniquely related to the convective heat flux. The model is then extended to the anelastic case as well as the fully compressible case. In the special case of spherical symmetry, the predicted radial heat flux is equivalent to that of mixing-length theory. For rotating stars, our model describes the coupled transport of heat and angular momentum, and provides a unified formalism in which to study both differential rotation and thermal inhomogeneities in stellar convection zones.