Convective instability in a rapidly rotating fluid layer in the presence of a non-uniform magnetic field

Magnetoconvective instabilities in a rapidly rotating, electrically conducting fluid layer heated from below in the presence of a non-uniform, horizontal magnetic field are investigated. It was first shown by Chandrasekhar that an overall minimum of the Rayleigh number may be reached at the onset of magnetoconvection when a uniform basic magnetic field is imposed. In this paper, we show that the properties of instability can be quite different when a non-uniform basic magnetic field is applied. It is shown that there is an optimum value of the Elsasser number provided that the basic magnetic field is a monotonically decreasing or increasing function of the vertical coordinate. However, there exist no optimum values of the Elsasser number that can give rise to an overall minimum of the Rayleigh number at the onset of magnetoconvection if the imposed basic magnetic field has an inflexion point. The project supported by the National Natural Science Foundation of China (40174026 and 40074041)     

一种适用于磁流体力学切向间断的HLLC黎曼算子

磁场的存在使得磁流体力学特征波模不同于流体力学, 因此直接由流体力学HLLC黎曼算子导出的HLLC双中间态在交界的间断面会出现不守恒的问题。通常降级采用HLL单磁场中间态代替HLLC双磁场中间态以实现守恒和计算稳定, 代价是切向间断的模拟精度不足。本文对此进行改进, 在模拟切向间断时仍然保留原有的HLLC双磁场中间态, 同时各守恒量仍然能够满足Toro相容条件; 改进型HLLC算子在间断两侧的磁场分量存在差异, 因此能够更精确还原切向间断面。基于数值测试, 包括一维激波管和切向间断的时变模拟, 以及地球磁层三维数值模拟, 将模拟结果进行对比, 结果表明: 相比于已发展的HLLC算子, 改进型HLLC算子对切向间断具有更好的捕捉精度, 能够达到或接近耗时更多的HLLD算子的模拟精度。     

Oscillation of Quasi-Steady Earth＇s Magnetosphere

A three-dimensional magnetohydrodynamics （MHD） code is designed specially for global simulations of the solar wind-magnetosphere-ionosphere system. The code possesses a high resolution in capturing MHD shocks and discontinuities and a low numerical dissipation in examining possible instabilities inherent in the system. The ionosphere is approximated by a spherical shell with uniform height-integrated conductance. The solar wind is steady, and the interplanetary magnetic field is either due northward or due southward. The code is then run to find solutions of the whole system. It is found that the system has never reached a steady state, but keeps oscillating with a period of about one hour in terms of density variation at the geosynchronous orbit. However, if a certain artificial resistivity is added either in the whole numerical box or in the reconnection sites only, the reconnections change from intermittent to steady regime and the oscillation disappears accordingly. We conclude that the Earth＇s magnetosphere tends to be in a ceaseless oscillation status because of the low dissipation property inherent in the magnetospheric plasma, and the oscillation may be driven by intermittent magnetic reconnections that occur somewhere in the magnetopause and/or the magnetotail.     

Earth＇s Magnetosphere Impinged by Interplanetary Shocks of Different Orientations

Using a recently developed PPMLR-MHD code, we carry out a global numerical simulation of the interaction between interplanetary shocks and Earth＇s magnetosphere. The initial magnetosphere is in a quasi-steady state, embedded in a uniform solar wind and a spiral interplanetary magnetic field （IMF）. An interplanetary （IP） shock interacts in turn with the bow shock, the magnetosheath, the magnetopause, and the magnetosphere, and changes the magnetosphere in shape and structure, and the distribution of the electric current and potential in the ionosphere as well. A preliminary comparison is made between two IP shocks of the same solar wind dynamic pressure and a vanishing IMF Bz on the downstream side, but with different propagation directions, one parallel and the other oblique to the Sun-Earth line. The numerical results show that both shocks cause a compression of the magnetosphere, an enhancement of magnetic field strength and field-aligned current in the magnetosphere, and an increase of the dawn-dusk electric potential drops across the polar ionosphere. Moreover, the magnetosphereionosphere system approaches a similar quasi-steady state after the interaction, for the downstream states are very close for the two shocks. However, the evolution processes of the system are remarkably different during the interaction with the two shocks of different orientations. The shock with the normal oblique to the Sun-Earth line results in a much longer evolution time for the system. This demonstrates that the shock orientation plays an important role in determining the associated geophysical effects and interpreting multisatellite observations of IP shock-magnetosphere interaction events.