磁瑞利-泰勒不稳定性非线性演化数值模拟

Numerical Simulation on Nonlinear Evolution of Magneto-Rayleigh-Taylor Instability

基于理想磁流体力学模型,采用5阶WENO有限差分格式结合磁场伪散度清除投影算法,发展二维数值模拟程序,利用线性理论对程序进行检验,在此基础上研究磁瑞利-泰勒(MRT)不稳定性非线性演化物理过程和发展规律。结果表明:垂直于加速度方向磁场在线性和非线性阶段对MRT扰动发展都有较强的制稳作用,而平行于加速度方向磁场在线性阶段对MRT扰动发展影响较小,但在MRT扰动非线性发展阶段会对由于流场变化产生的K-H不稳定性有显著的制稳作用,从而抑制总的扰动发展。在MRT非线性发展过程中,由于波模耦合相互作用,单模演化会产生高次谐波;双模演化会产生除基模和谐波以外的其他波模,其扰动幅度甚至超过基模;多模演化过程中发生逆级联过程,即短波长扰动逐渐向长波长扰动发展。

A 2 D numerical simulation program is developed for nonlinear evolution of magneto-Rayleigh-Taylor instability(MRTI).Based on an ideal magnetohydrodynamic model,a 5 th WENO scheme is employed to calculate MHD equations and a projection scheme is used to clean spurious magnetic field divergence.The method is validated with MRTI compared with theory of linear stability.It is shown that the vertical magnetic field suppresses evidently MRTI in both linear and nonlinear stages.The parallel magnetic field has weak effect on MRTI in linear stage.However,it reduces remarkably Kelvin-Helmholtz instability and overall instability in nonlinear regime.High order harmonic occurs in the nonlinear evolution of single mode,and many modes except fundamental modes and harmonic occur in the evolution of double modes.In MRT evolution of multi-mode seeds inverse cascade occur,which means that perturbations evolve from short wavelength to long wavelength in the nonlinear stage.