有外加磁场的viscous fluid旋转层中对流的开始：对普朗特数的依赖
The onset of convection in a rotating layer of viscous fluid with an imposed magnetic field: dependence on the Prandtl numbers
摘要：
本文研究了具有刚性电绝缘水平边界的导电不可压缩流体水平层中的Boussinesq对流。流体从下方被加热并围绕垂直轴旋转;施加垂直磁场。平凡的稳定状态（流体静止）的不稳定性可以是单调的或振荡的，这取决于问题的参数（运动学和磁普朗特，泰勒和Prandtlasekhar数）。如果泰勒数足够大，出现在单调不稳定中的对流卷将经历库珀斯-洛茨不稳定。我们研究了临界瑞利数、平凡定态的不稳定性类型以及Küppers-Lortz不稳定性的临界泰勒数与普朗特数的关系。我们认为普朗特数不超过1，这是典型的内核的地球。
英文摘要：
We consider the onset of Boussinesq convection in a horizontal layer of electrically conducting incompressible fluid with rigid electrically insulating horizontal boundaries. The fluid is heated from below and rotates about a vertical axis; vertical magnetic field is imposed. The instability of the trivial steady state (fluid at rest) can be monotonic or oscillatory depending on parameters of the problem (the kinematic and magnetic Prandtl, Taylor and Chandrasekhar numbers). If the Taylor number is sufficiently large, convective rolls, emerging in the monotonic instability, experience the Küppers-Lortz instability. We study how the critical Rayleigh number, the type of instability of the trivial steady state and the critical Taylor number for the Küppers-Lortz instability depend on the Prandtl numbers. We consider Prandtl numbers not exceeding one, which is typical for the inner core of the Earth.
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