Reynolds-number dependence of the dimensionless dissipation rate in homogeneous magnetohydrodynamic turbulence

TL;DR

This study investigates how the dimensionless energy dissipation rate in homogeneous magnetohydrodynamic turbulence depends on Reynolds number, considering both stationary and nonstationary conditions, and explores the effects of external forces and helicities.

Contribution

The paper develops a general model for the dissipation rate in homogeneous MHD turbulence and provides comprehensive numerical validation across different turbulence regimes.

Findings

Asymptotic dissipation rate between 0.193 and 0.268 depending on initial helicities.

Stationary turbulence dissipation rate measured at 0.223.

Reynolds number influences the energy dissipation rate and nonuniversality is affected by external forces and helicities.

Abstract

This paper examines the behavior of the dimensionless dissipation rate $C_{\varepsilon}$ for stationary and nonstationary magnetohydrodynamic (MHD) turbulence in presence of external forces. By combining with previous studies for freely decaying MHD turbulence, we obtain here both the most general model equation for $C_{\varepsilon}$ applicable to homogeneous MHD turbulence and a comprehensive numerical study of the Reynolds number dependence of the dimensionless total energy dissipation rate at unity magnetic Prandtl number. We carry out a series of medium to high resolution direct numerical simulations of mechanically forced stationary MHD turbulence in order to verify the predictions of the model equation for the stationary case. Furthermore, questions of nonuniversality are discussed in terms of the effect of external forces as well as the level of cross- and magnetic helicity. The measured values of the asymptote $C_{\varepsilon,\infty}$ lie between $0.193 \leqslant C_{\varepsilon,\infty} \leqslant 0.268$ for free decay, where the value depends on the initial level of cross- and magnetic helicities. In the stationary case we measure $C_{\varepsilon,\infty} = 0.223$.