Angular momentum transport in convectively unstable shear flows

TL;DR

This study investigates how hydrodynamic turbulent convection influences angular momentum transport in shear flows, revealing the roles of turbulent viscosity and the Lambda-effect, and showing conditions under which transport can be outward in Keplerian regimes.

Contribution

The paper introduces a combined numerical and analytical approach to quantify turbulent viscosity and the Lambda-effect in convective shear flows, highlighting their dependence on rotation and shear parameters.

Findings

Turbulent viscosity is comparable to mixing length estimates and weakly affected by rotation.

The Lambda-effect is present and smaller than turbulent viscosity in slow rotation.

Angular momentum transport can be outward in Keplerian shear when the rotation period exceeds the turnover time.

Abstract

Angular momentum transport owing to hydrodynamic turbulent convection is studied using local three dimensional numerical simulations employing the shearing box approximation. We determine the turbulent viscosity from non-rotating runs over a range of values of the shear parameter and use a simple analytical model in order to extract the non-diffusive contribution (Lambda-effect) to the stress in runs where rotation is included. Our results suggest that the turbulent viscosity is of the order of the mixing length estimate and weakly affected by rotation. The Lambda-effect is non-zero and a factor of 2-4 smaller than the turbulent viscosity in the slow rotation regime. We demonstrate that for Keplerian shear, the angular momentum transport can change sign and be outward when the rotation period is greater than the turnover time, i.e. when the Coriolis number is below unity. This result seems to be relatively independent of the value of the Rayleigh number.