Department of Physics & INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy.
SUPA, School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, EH9 3FD, United Kingdom.
Phys Rev E. 2017 Jan;95(1-1):013102. doi: 10.1103/PhysRevE.95.013102. Epub 2017 Jan 4.
This paper examines the behavior of the dimensionless dissipation rate C_{ɛ} for stationary and nonstationary magnetohydrodynamic (MHD) turbulence in the 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_{ɛ} 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_{ɛ,∞} lie between 0.193≤C_{ɛ,∞}≤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_{ɛ,∞}=0.223.
本文研究了在外部力作用下，定常和非定常磁流体力学（MHD）湍流的无量纲耗散率 C_{ɛ}的行为。通过与先前关于自由衰减 MHD 湍流的研究相结合，我们得到了适用于均匀 MHD 湍流的最通用的 C_{ɛ}模型方程，以及在单位磁普朗特数下，对无量纲总能量耗散率与雷诺数关系的全面数值研究。我们进行了一系列中等至高分辨率的机械强迫定常 MHD 湍流的直接数值模拟，以验证定常情况下模型方程的预测。此外，还讨论了非普遍性问题，涉及外部力的影响以及交叉和磁螺旋度的水平。对于自由衰减，测量得到的渐近值 C_{ɛ,∞}在 0.193≤C_{ɛ,∞}≤0.268 之间，其值取决于初始的交叉和磁螺旋度水平。在定常情况下，我们测量到 C_{ɛ,∞}=0.223。
