二维不可压粘性两相流瑞利-泰勒不稳定性的临界磁场

Critical magnetic field of Rayleigh-Taylor instability in two-dimensional incompressible viscous two-phase flow

讨论了两层互不相溶的不可压粘性流体和无磁扩散的磁流体组成的系统的RT不稳定性问题.在拉格朗日坐标系下利用流映射重写了磁场中的洛伦兹力;通过在稳态解附近做线性化,得到线性方程组;为了研究流体稳定性,利用法向模式解,将问题转换成特征值问题;因为流体具有粘性,用修正的变分法解特征值问题,得到了二维情形下垂直磁场使系统致稳的临界磁场和临界频率;当所给磁场大于临界磁场时,系统稳定;当所给磁场小于临界磁场时,在低频时,系统仍然稳定,但高频时,系统不稳定.

The RT instability for two immiscible,incompressible,viscous fluid and magnetic fluid with zero resistivity is discussed.The Lorentz force in the magnetic field is rewritten by flow mapping in the Lagrangian coordinate system.The linear equations are obtained by linearizing near the steady-state solution.In order to study the stability of the fluid,the normal mode solution is used to transform the problem into an eigenvalue problem.Because the fluid is viscous,the modified variational method is used to solve the eigenvalue problem,and the critical magnetic field and critical frequency of the system stabilized by vertical magnetic field in two-dimensional case are obtained.When the given magnetic field is greater than the critical magnetic field,the system is stable;when the given magnetic field is less than the critical magnetic field,the system is still stable at low frequency,but unstable at high frequency.