Direct Calculation of the Turbulent Dissipation Efficiency in Anelastic Convection

TL;DR

This paper directly calculates the turbulent dissipation efficiency in anelastic stellar convection, especially for cases outside Kolmogorov scaling, providing new data and methods for astrophysical turbulence modeling.

Contribution

It introduces a direct simulation approach to determine turbulent dissipation efficiency in regimes where Kolmogorov scaling does not apply, and compares results with existing perturbative methods.

Findings

Effective viscosity varies with perturbation frequency.

Results extend understanding of turbulence in stellar convective zones.

Comparison with perturbative methods validates the approach.

Abstract

The current understanding of the turbulent dissipation in stellar convective zones is based on the assumption that the turbulence follows Kolmogorov scaling. This assumption is valid for some cases in which the time frequency of the external shear is high (e.g., solar p modes). However, for many cases of astrophysical interest (e.g., binary orbits, stellar pulsations, etc.), the timescales of interest lie outside the regime of applicability of Kolmogorov scaling. We present direct calculations of the dissipation efficiency of the turbulent convective flow in this regime, using simulations of anelastic convection with external forcing. We show that the effects of the turbulent flow are well represented by an effective viscosity coefficient, we provide the values of the effective viscosity as a function of the perturbation frequency and compare our results to the perturbative method for finding the effective viscosity of Penev et al. that can be applied to actual simulations of the surface convective zones of stars.