Theory and modeling of hydromagnetic instabilities

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1. By two-dimensional hydrodynamic and hydromagnetic simulations of Kelvin-Helmholtz instability it has been shown that vortices excited by the instability merge in the nonlinear stage. In the hydromagnetic case a current eddy is associated with each vortex. The vortex pairing occurring in th nonlinear stage has been shown to be a self-organization process, wherein the total kinetic energy is conserved but the enstrophy decays rapidly to the minimum enstrophy state. The self-organization occurs owing to the inverse cascade of kinetic energy in the wave-number space.The momentum transport depends on the self-organization and the anomalous momentum transport in increases with a development of the self-organization. The observational fact that the magnetopause oscillation period increases with increasing distance in the downstream can be explained quantitatively by the simulation results showing the pairing of vortices in the nonlinear stage.2. On the basis of the MHD energy principle and the perturbation analysis it has been shown that incompressible assumption is more valid for the ballooning instability when the manetosphere becomes more tail-like. This justifies an early linear analysis of the ballooning instability in the tail-like configuration based on incompressible assumption. This result suggests that the ballooning instability may be relevant to the onset of magnetospheric substorms, which occur when the magnetosphere becomes tail-like in the night-side.