Simon P, Sahraoui F
Laboratoire de Physique des Plasmas (LPP), CNRS, Observatoire de Paris, Sorbonne Université, Université Paris-Saclay, École polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau, France.
Phys Rev E. 2022 May;105(5-2):055111. doi: 10.1103/PhysRevE.105.055111.
We derive an exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence. For a gyrotropic pressure tensor, we study the double-adiabatic case and show the presence of new flux and source terms in the exact law, reminiscent of the plasma instability conditions due to pressure anisotropy. The Hall term is shown to bring ion-scale corrections to the exact law without affecting explicitly the pressure terms. In the pressure isotropy limit we recover all known results obtained for isothermal and polytropic closures. The incompressible limit of the gyrotropic system leads to a generalization of the Politano and Pouquet's law where a new incompressible source term is revealed and reflects exchanges of the magnetic and kinetic energies with the no-longer-conserved internal energy. We highlight the possibilities offered by the new laws to investigate potential links between turbulence cascade and instabilities widely observed in laboratory and astrophysical plasmas.
我们推导了可压缩压力各向异性磁流体动力学湍流的精确定律。对于回转各向异性压力张量，我们研究了双绝热情况，并表明精确定律中存在新的通量项和源项，这让人联想到由于压力各向异性导致的等离子体不稳定性条件。结果表明，霍尔项给精确定律带来了离子尺度修正，而没有明确影响压力项。在压力各向同性极限下，我们恢复了所有通过等温及多方闭合得到的已知结果。回转各向异性系统的不可压缩极限导致了波利塔诺和普凯定律的推广，其中揭示了一个新的不可压缩源项，它反映了磁能和动能与不再守恒的内能之间的交换。我们强调了新定律为研究实验室和天体物理等离子体中广泛观察到的湍流级联与不稳定性之间的潜在联系所提供的可能性。
