Universität zu Köln, Institut für Geophysik und Meteorologie, Pohligstrasse 3, 50969 Köln, Germany.
University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0424, USA.
Phys Rev E. 2018 Feb;97(2-1):023107. doi: 10.1103/PhysRevE.97.023107.
Three-dimensional, compressible, magnetohydrodynamic turbulence of an isothermal, self-gravitating fluid is analyzed using two-point statistics in the asymptotic limit of large Reynolds numbers (both kinetic and magnetic). Following an alternative formulation proposed by Banerjee and Galtier [Phys. Rev. E 93, 033120 (2016)2470-004510.1103/PhysRevE.93.033120; J. Phys. A: Math. Theor. 50, 015501 (2017)1751-811310.1088/1751-8113/50/1/015501], an exact relation has been derived for the total energy transfer. This approach results in a simpler relation expressed entirely in terms of mixed second-order structure functions. The kinetic, thermodynamic, magnetic, and gravitational contributions to the energy transfer rate can be easily separated in the present form. By construction, the new formalism includes such additional effects as global rotation, the Hall term in the induction equation, etc. The analysis shows that solid-body rotation cannot alter the energy flux rate of compressible turbulence. However, the contribution of a uniform background magnetic field to the flux is shown to be nontrivial unlike in the incompressible case. Finally, the compressible, turbulent energy flux rate does not vanish completely due to simple alignments, which leads to a zero turbulent energy flux rate in the incompressible case.
采用两点统计方法，在大雷诺数（包括动能和磁能）的渐近极限下，分析了等温、自引力流体的三维可压缩磁流体力学湍流。Banerjee 和 Galtier [Phys. Rev. E 93, 033120 (2016)2470-004510.1103/PhysRevE.93.033120; J. Phys. A: Math. Theor. 50, 015501 (2017)1751-811310.1088/1751-8113/50/1/015501] 提出了一种替代公式，推导出了总能量传递的精确关系。这种方法导致了一个更简单的关系，完全用混合二阶结构函数表示。在目前的形式下，可以很容易地将动能、热力学、磁场和引力对能量传递率的贡献分开。通过构造，新的形式主义包括了全局旋转、感应方程中的 Hall 项等额外效应。分析表明，刚体旋转不能改变可压缩湍流的能量通量率。然而，与不可压缩情况不同，均匀背景磁场对通量的贡献并非微不足道。最后，由于简单的排列，可压缩湍流的能量通量率不会完全消失，这导致不可压缩情况下的湍流能量通量率为零。
