Lambda-effect from forced turbulence simulations

TL;DR

This study uses numerical simulations to analyze the Lambda-effect tensor in turbulent momentum transport under rotation, revealing key stress behaviors relevant to stellar convection zones and comparing results with analytical models.

Contribution

It provides the first detailed numerical investigation of the Lambda-effect tensor components in forced turbulence simulations, validating the minimal tau-approximation approach.

Findings

Vertical stress is negative when vertical turbulence dominates.

Horizontal stress peaks at 30 degrees latitude regardless of rotation speed.

Minimal tau-approximation qualitatively matches numerical results when tau is near the turnover time.

Abstract

Aims: We determine the components of the $\Lambda$-effect tensor that quantifies the contributions to the turbulent momentum transport even for uniform rotation. Methods: Three-dimensional numerical simulations are used to study turbulent transport in triply periodic cubes under the influence of rotation and anisotropic forcing. Comparison is made with analytical results obtained via the so-called minimal tau-approximation. Results: In the case where the turbulence intensity in the vertical direction dominates, the vertical stress is always negative. This situation is expected to occur in stellar convection zones. The horizontal component of the stress is weaker and exhibits a maximum at latitude 30 degrees - regardless of how rapid the rotation is. The minimal tau-approximation captures many of the qualitative features of the numerical results, provided the relaxation time tau is close to the turnover time, i.e. the Strouhal number is of order unity.