Mean-field theory of differential rotation in density stratified turbulent convection

TL;DR

This paper develops a mean-field theory for differential rotation in density-stratified turbulent convection, incorporating turbulent heat flux and anisotropy, and successfully predicts solar-like rotation profiles.

Contribution

It introduces a coupled system of dynamical equations solved with the spectral tau approach, accounting for rotation effects on turbulence anisotropy and correlation time.

Findings

The theory predicts radial differential rotation profiles matching solar observations.

It demonstrates the impact of turbulent heat flux and anisotropy on differential rotation.

The model is valid for high Reynolds and Peclet numbers.

Abstract

A mean-field theory of differential rotation in a density stratified turbulent convection has been developed. This theory is based on a combined effect of the turbulent heat flux and anisotropy of turbulent convection on the Reynolds stress. A coupled system of dynamical budget equations consisting in the equations for the Reynolds stress, the entropy fluctuations and the turbulent heat flux has been solved. To close the system of these equations, the spectral tau approach which is valid for large Reynolds and Peclet numbers, has been applied. The adopted model of the background turbulent convection takes into account an increase of the turbulence anisotropy and a decrease of the turbulent correlation time with the rotation rate. This theory yields the radial profile of the differential rotation which is in agreement with that for the solar differential rotation.