LPP, CNRS, Ecole Polytechnique, UPMC Université Paris 06, Université Paris-Sud, Observatoire de Paris, Université Paris-Saclay, Sorbonne Universités, PSL Research University, F-91128 Palaiseau, France.
Phys Rev E. 2017 Nov;96(5-1):053205. doi: 10.1103/PhysRevE.96.053205. Epub 2017 Nov 20.
The exact law for fully developed homogeneous compressible magnetohydrodynamics (CMHD) turbulence is derived. For an isothermal plasma, without the assumption of isotropy, the exact law is expressed as a function of the plasma velocity field, the compressible Alfvén velocity, and the scalar density, instead of the Elsasser variables used in previous works. The theoretical results show four different types of terms that are involved in the nonlinear cascade of the total energy in the inertial range. Each category is examined in detail, in particular, those that can be written either as source or flux terms. Finally, the role of the background magnetic field B_{0} is highlighted and a comparison with the incompressible MHD (IMHD) model is discussed. This point is particularly important when testing this exact law on numerical simulations and in situ observations in space plasmas.
已推导完全发展均匀可压磁流体力学（CMHD）湍流的确切定律。对于各向同性的等离体，无需各向同性假设，该确切定律可表示为等离子体速度场、可压阿尔芬速度和标量密度的函数，而不是之前工作中使用的埃尔斯拉斯变量。理论结果表明，在惯性范围内总能量的非线性级联中涉及四种不同类型的项。详细检查了每种类别，特别是可以表示为源项或通量项的类别。最后，强调了背景磁场 B_{0} 的作用，并讨论了与不可压磁流体力学（IMHD）模型的比较。当在空间等离子体的数值模拟和原位观测中检验这个确切定律时，这一点尤为重要。
