Reynolds stress and heat flux in spherical shell convection

TL;DR

This study compares turbulent angular momentum and heat fluxes in spherical and Cartesian convection models across different rotation rates, revealing how rotation influences turbulent transport and differential rotation profiles in stellar convection zones.

Contribution

It extends previous Cartesian studies by using spherical wedge simulations to analyze turbulent fluxes as functions of rotation, clarifying the reproduction of equatorial Reynolds stress profiles in spherical models.

Findings

Radial and latitudinal fluxes are inward and equatorward at slow rotation.

Radial flux sign reverses at rapid rotation, contradicting theory.

Heat flux shifts from equatorward to poleward with increasing rotation.

Abstract

(abridged) Context. Turbulent fluxes of angular momentum and heat due to rotationally affected convection play a key role in determining differential rotation of stars. Here we perform a systematic comparison between Cartesian and spherical geometries as a function of the rotation rate. Aims. We extend the earlier studies by using spherical wedges to obtain turbulent angular momentum and heat transport as functions of the rotation rate from stratified convection. We compare results from spherical and Cartesian models in the same parameter regime. In particular, we want to clarify whether the sharp equatorial profile of the horizontal Reynolds stress found in earlier Cartesian models is reproduced in spherical models. Methods. We employ direct numerical simulations of turbulent convection. In order to reach as high spatial resolution as possible in the spherical runs, we model only parts of the latitude and longitude. The rotational influence, measured by the Coriolis number, is varied from zero to roughly seven, which is the regime that is likely to be realised in the solar convection zone. Cartesian simulations are performed in overlapping parameter regimes. Results. For slow rotation we find that the radial and latitudinal turbulent angular momentum fluxes are directed inward and equatorward, respectively. In the rapid rotation regime the radial flux changes sign in contradiction with theory. The latitudinal flux remains mostly equatorward and develops a maximum close to the equator. In Cartesian simulations this peak can be explained by the strong `banana cells'. The latitudinal heat flux is mostly equatorward for slow rotation but changes sign for rapid rotation. The rotation profiles vary from anti-solar (slow equator) for slow and intermediate rotation to solar-like (fast equator) for rapid rotation. The solar-like profiles are dominated by the Taylor--Proudman balance.