On Linear Instability and Stability of the Rayleigh-Taylor Problem in Magnetohydrodynamics
On Linear Instability and Stability of the Rayleigh-Taylor Problem in Magnetohydrodynamics
复制标题
磁流体动力学中瑞利-泰勒问题的线性不稳定性和稳定性
DOI：
10.1007/s00021-015-0221-x
复制
发表时间：
2015
影响因子：
1.3
通讯作者：
Jiang Song
中科院分区：
文献类型：
--
作者：
Jiang Fei;Jiang Song
研究了在三维有界区域中，在均匀重力场作用下，非均匀不可压缩粘性零电阻率磁流体的线性化Rayleigh-Taylor（RT）问题中磁场的稳定作用，其中流体的速度在边界上是无滑移的.通过调整一个修改的变分方法和仔细推导先验估计，我们建立了一个标准的不稳定性/稳定性的线性化问题周围的磁RT平衡状态。在该判据中，我们发现了一个新的现象，即足够强的水平磁场对磁RT不稳定性的增长具有与垂直磁场相同的稳定作用。此外，我们进一步研究了相应的可压缩情况，即，帕克（或磁浮力）问题，其中水平磁场的强度随高度而减小，并且还显示了足够大的磁场的稳定效果。
We investigate the stabilizing effects of the magnetic fields in the linearized magnetic Rayleigh–Taylor (RT) problem of a nonhomogeneous incompressible viscous magnetohydrodynamic fluid of zero resistivity in the presence of a uniform gravitational field in a three-dimensional bounded domain, in which the velocity of the fluid is non-slip on the boundary. By adapting a modified variational method and careful deriving a priori estimates, we establish a criterion for the instability/stability of the linearized problem around a magnetic RT equilibrium state. In the criterion, we find a new phenomenon that a sufficiently strong horizontal magnetic field has the same stabilizing effect as that of the vertical magnetic field on growth of the magnetic RT instability. In addition, we further study the corresponding compressible case, i.e., the Parker (or magnetic buoyancy) problem, for which the strength of a horizontal magnetic field decreases with height, and also show the stabilizing effect of a sufficiently large magnetic field.