论文标题
正弦剪切流中的电阻不稳定性用流向磁场
Resistive instabilities in sinusoidal shear flows with a streamwise magnetic field
论文作者
论文摘要
我们研究了具有有限的电阻率和粘度的不可压缩磁性水力学（MHD）的框架中最初具有均匀流动磁场的正弦剪切流的线性稳定性。在流体动力学病例中，该流量与开尔文 - 霍尔姆兹不稳定是不稳定的。在理想的MHD中，忽略耗散的理想MHD也是如此，前提是磁场强度不超过磁场的临界阈值，而磁张力可以稳定流动。在这里，我们证明包括粘度和电阻率引入了两种新的不稳定性模式。只要磁性prandtl number $ pm <1 $，就存在这些模式之一，我们称之为不稳定的alfvén波，它与剪切alfvén波的联系而存在。我们提出了这种不稳定性的简化模型，该模型揭示其激发机制是Dubrulle＆Frisch（1991）描述的周期性剪切流的负涡流粘度。最后，我们从数值上证明，这种模式在以反传播孤子子为主的准平台状态中饱和。
We investigate the linear stability of a sinusoidal shear flow with an initially uniform streamwise magnetic field in the framework of incompressible magnetohydrodynamics (MHD) with finite resistivity and viscosity. This flow is known to be unstable to the Kelvin-Helmholtz instability in the hydrodynamic case. The same is true in ideal MHD, where dissipation is neglected, provided the magnetic field strength does not exceed a critical threshold beyond which magnetic tension stabilizes the flow. Here, we demonstrate that including viscosity and resistivity introduces two new modes of instability. One of these modes, which we call a resistively-unstable Alfvén wave due to its connection to shear Alfvén waves, exists for any nonzero magnetic field strength as long as the magnetic Prandtl number $Pm < 1$. We present a reduced model for this instability that reveals its excitation mechanism to be the negative eddy viscosity of periodic shear flows described by Dubrulle & Frisch (1991). Finally, we demonstrate numerically that this mode saturates in a quasi-stationary state dominated by counter-propagating solitons.
