Modeling of the Hydromagnetic Instability

1.由于磁层顶零阶磁场的连续旋转，磁鞘磁场向北时比向南时更容易激发Kelvin-Helmholtz（K-H）不稳定性。当磁鞘磁场偏北时，由于K-H不稳定性的动量输运，磁层顶的速度边界层厚度变大。当磁鞘磁场不偏北时，在涡旋附近形成一个缓慢的稀薄区，等离子体在此区域被稀薄化，并沿磁力线沿着加速.导出了二维可压缩等离子体（流体）横向于磁场运动的涡度拟能守恒律。对磁场横向于流速的二维横向位形的MHD模拟表明，在K-H不稳定性的非线性阶段，由于涡旋配对，输运的动量和反常粘滞系数比线性增长最快的涡旋所产生的动量和反常粘滞系数大得多。在涡旋内部，等离子体被快速的磁声稀薄作用强烈地稀薄化，涡旋内部的磁压降低。在K-H不稳定性的作用下，旋涡周围的流速增加.在三维磁层-电离层耦合系统中，当电离层电导率大于某一临界电导率时，K-H不稳定性被完全抑制，该临界电导率几乎等于沿场线沿着平均的Alfven电导。这是由于磁层中的横向磁场的稳定影响，这是由横向电场引起的剪切速度流在磁层中产生的。

1. Owing to the continuous rotation of the zero-th order magnetic field across the magnetopause the Kelvin-Helmholtz (K-H) instability is more easily excited when the magnetosheath magnetic field is northward than when it is southward. The thickness of the velocity boundary layr at the magnetopause becomes larger when the magnetosheath magnetic field is northward owing to the momentum transport by the K-H instability. When the magnetosheath magnetic field is not due north, a slow rarefaction region is formed near the vortex, wherein the plasma is rarefied and accelerated along the field line.2. The conservation law of the enstrophy is derived for the 2-D compressible plasma (fluid) motion transverse to the magnetic field. An MHD simulation for the 2-D transverse configuration, where the magnetic field is transverse to the flow velocity, shows that owing to the vortex pairing in the nonlinear stage of the K-H instability the transported momentum and the anomalous viscosity become much larger than those due to the linearly fastest growing vortex. Inside the vortex the plasma is rarefied strongly by the fast magnetosonic rarefaction and the magnetic pressure is reduced inside the vortex. The flow velocity is enhanced at the periphery of the vortex, which is formed by the K-H instability.3. In the 3-D magnetosphere-ionosphere coupling system the K-H instability is suppressed completely when the ionospheric conductivity is higher than a critical conductivity, which is nearly equal to the Alfven conductance averaged along the field line. This is due to a stabilizing influence of the transverse magnetic field in the magnetosphere, which is produced by the transverse electric field causing the sheared velocity flow in the magnetosphere.