Critical magnetic number in the magnetohydrodynamic Rayleigh-Taylor instability
Critical magnetic number in the magnetohydrodynamic Rayleigh-Taylor instability
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DOI：
10.1063/1.4731479
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发表时间：
2012-07
影响因子：
1.3
通讯作者：
Yanjin Wang
中科院分区：
文献类型：
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作者：
Yanjin Wang
本文研究了磁流体力学方程组在无限大平板中的两相自由边界问题，其中流体被假定为不可压缩的、粘性的和零电阻率的。我们在拉格朗日坐标系中工作，以便根据流体流动图重写洛伦兹力。该方程允许一个稳态解，上层流体比下层流体重，这使得系统容易受到瑞利-泰勒不稳定性。我们研究的稳定效果的磁场的解决方案，通过线性化得到的方程在此稳态解。我们确定了临界磁数|B| c是一个变分问题。当磁场B <$在2D或3D中是垂直的并且当B <$在2D中是水平的时，我们证明了线性系统是稳定的，|B| ≥| B| c，不稳定，当|B| <|B| C.而且对于|B| <|B| c垂直B '稳定低频区间，而水平B'稳定高频区间，生长模式的生长速度..
We study the two-phase free boundary problem for the equations of magnetohydrodynamics in an infinite slab, where the fluids are assumed to be incompressible, viscous, and of zero resistivity. We work in Lagrangian coordinates so as to rewrite the Lorentz force in terms of the fluid flow map. The equations admit a steady-state solution with the upper fluid heavier than the lower fluid, which makes the system susceptible to the Rayleigh-Taylor instability. We study the stabilizing effect of the magnetic field on solutions to the equations obtained by linearizing around this steady-state solution. We identity the critical magnetic number |B|c by a variational problem. When the magnetic field B¯ is vertical in 2D or 3D and when B¯ is horizontal in 2D we prove that the linear system is stable when |B¯|≥|B|c and is unstable when |B¯|<|B|c. Moreover, for |B¯|<|B|c the vertical B¯ stabilizes a low frequency interval while the horizontal B¯ stabilizes a high frequency interval, and the growth rate of growing mode...