引入磁场破坏Richardson判据
Violation of Richardson's Criterion via Introduction of a Magnetic Field
摘要：
剪切流不稳定性可以深刻地影响喷流、恒星和圆盘中动量的扩散。Richardson准则给出了分层介质中剪切流不稳定的一个充分条件。速度梯度$V'$仅能使具有平方Brunt-Vaisala频率$N^2$的稳定分层介质失稳，如果$V'^2/4>N^2$。我们发现，当介质是磁化等离子体时，这不再是真的。我们研究了稳定层结对磁场和速度分布的影响，这些磁场和速度分布对磁剪切不稳定性是不稳定的，即，需要同时存在磁场和剪切流的不稳定性。我们证明了Tatsuno & Dorland（2006）最初研究的一系列轮廓即使在$V'^2/4<N^2$时仍然不稳定，违反了Richardson准则。然而，并不是所有的磁场都能导致违反理查森准则。我们考虑一类最初由Kent（1968）提出的流动，它在恒定磁场作用下是不稳定的，并证明了当$V'^2/4<N^2$，如Richardson判据所预言的那样，它们变得稳定。这意味着需要磁自由能才能违反理查森判据。这项工作意味着，理查森标准不能使用时，评估剪切，稳定分层，磁化等离子体的理想稳定性。我们简要地讨论了天体物理系统的影响。
英文摘要：
Shear flow instabilities can profoundly affect the diffusion of momentum in jets, stars, and disks. The Richardson criterion gives a sufficient condition for instability of a shear flow in a stratified medium. The velocity gradient $V'$ can only destabilize a stably stratified medium with squared Brunt-Vaisala frequency $N^2$ if $V'^2/4>N^2$. We find this is no longer true when the medium is a magnetized plasma. We investigate the effect of stable stratification on magnetic field and velocity profiles unstable to magneto-shear instabilities, i.e., instabilities which require the presence of both magnetic field and shear flow. We show that a family of profiles originally studied by Tatsuno & Dorland (2006) remain unstable even when $V'^2/4<N^2$, violating the Richardson criterion. However, not all magnetic fields can result in a violation of the Richardson criterion. We consider a class of flows originally considered by Kent (1968), which are destabilized by a constant magnetic field, and show that they become stable when $V'^2/4<N^2$, as predicted by the Richardson criterion. This suggests that magnetic free energy is required to violate the Richardson criterion. This work implies that the Richardson criterion cannot be used when evaluating the ideal stability of a sheared, stably stratified, and magnetized plasma. We briefly discuss the implications for astrophysical systems.
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