Modeling of the Hydromagnetic Instability

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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.