Theory and modeling of hydromagnetic instabilities

1.通过对Kelvin-Helmholtz不稳定性的二维水动力和流体磁学模拟，发现由不稳定性激发的涡旋在非线性阶段合并。在流体磁学的情况下，每个涡旋都有一个电流涡旋。非线性阶段的涡旋配对是一个自组织过程，其中总动能是守恒的，而拟能迅速衰减到最小拟能态。自组织是由于波数空间动能的逆级联引起的，动量输运依赖于自组织，反常动量输运随着自组织的发展而增加。结果表明，在非线性阶段，磁层顶振荡周期随距离的增加而增大，这一现象可以定量地解释。根据MHD能量原理和摄动分析，证明了不可压缩假设对热气球不稳定更适用于尾部的情况。这证明了基于不可压缩假设对尾形构型中气球不稳定性的早期线性分析是正确的。这一结果表明，气球不稳定性可能与磁层亚暴的开始有关，亚暴发生在磁层在夜间变得像尾巴一样时。

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.