Reynolds number dependence of the dimensionless dissipation rate in stationary magnetohydrodynamic turbulence

etc15 Tracking Number 319

Results on the Reynolds number dependence of the dimensionless total dissipation rate C_ε are presented, obtained from medium to high resolution direct numerical simulations (DNSs) of mechanically forced stationary homogeneous magnetohydrodynamic (MHD) turbulence in the absence of a mean magnetic field, showing that C_ε -> const with increasing Reynolds number. Furthermore, a model equation for the Reynolds number dependence of the dimensionless dissipation rate is derived from the real-space energy balance equation by asymptotic expansion in terms of Reynolds number of the second- and third-order correlation functions of the Elsässer fields z± = u ± b. At large Reynolds numbers we find that a model of the form C_ε = C_ε,∞ + C/R describes the data well, while at lower Reynolds numbers the model needs to be extended to second order in 1/R in order to obtain a good fit to the data, where R is a generalised Reynolds number with respect to the Elsässer field z-.