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

Abstract

This paper examines the behavior of the dimensionless dissipation rate $C_{\epsilon }$ 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 $C_{\epsilon }$ 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 $C_{\epsilon ,\infty }$ lie between $0.193⩽C_{\epsilon ,\infty }⩽0.268$ for free decay, where the value depends on the initial level of cross- and magnetic helicities. In the stationary case we measure $C_{\epsilon ,\infty }=0.223$.

arXiv comment18 pages, 2 figures

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