双层Kidder自相似解及其Rayleigh-Taylor不稳定性研究

Linear Rayleigh-Taylor Instability Analysis of a Double-Shell Kidder's Self-Similar Implosion

将单层Kidder自相似解推广到双层,使得两层壳体的交界面两侧存在密度跳跃,使得轻流体向重流体加速产生Rayleigh-Taylor不稳定性;通过采用Lagrange坐标下的Godunov方法进行一维直接数值模拟,将模拟解与双层Kidder自相似基本解进行比较,验证了双层Kidder自相似解的可靠性;最后,通过编制球形内爆的三维扰动的线性稳定性分析程序,对双层Kidder自相似解的Rayleigh-Taylor不稳定性进行了分析计算.计算结果表明:初始扰动越集中于交界面,会造成后期扰动增长得越快,越不稳定;扰动波数越大,扰动增长得越快,越不稳定;从扰动在空间上的发展来看,可压缩性研究表明内外壳体的可压缩性对扰动增长起着相反的作用,外层壳体的可压缩性对Rayleigh-Taylor不稳定起失稳作用,而内层壳体的可压缩性对Rayleigh-Taylor不稳定起致稳作用.

By generalizing the single-shell Kidder＇ s self-similar solution to double-shell with a discontinuity for density across the interface, an isentropic implosion model was constructed to study the Rayleigh-Taylor instability for the implosion compression. A Godunov-type method in Lagranglan coordinates was used to compute the one-dimensional Euler equation with the initial conditions and boundary conditions of the double-shell Kidder＇ s serf-similar solution in spherical geometry, and numerical results were obtained to validate the double-shell implosion model. By programming and using the linear perturbation code, a linear stability analysis on the Rayleigh-Taylor instability for the double-shell isentropic implosion model was performed. It is found that when the initial perturbation concentrates much closer to the interface of the two shells, or when the spherical wave number becomes much smaller, the interface modal radius grows much faster, i.e. more unstable. In addition, from the spatial point of view for the compressibility effect on the perturbation evolution, it is found that the compressibility of the outer shell has destabilization effect on Rayleigh-Taylor instability, while the compressibility of the inner shell has stabilization effect.