Nonlinear evolution of an interface in the Richtmyer-Meshkov instability.
Nonlinear evolution of an interface in the Richtmyer-Meshkov instability.
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DOI：
10.1103/physreve.67.036301
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发表时间：
2003-03
期刊：
影响因子：
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通讯作者：
C. Matsuoka;K. Nishihara;Y. Fukuda
中科院分区：
文献类型：
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作者：
C. Matsuoka;K. Nishihara;Y. Fukuda
Wouchuk和Nishihara提出的Richtmyer-Meshkov不稳定性的线性理论等离子体4,3761(1997)]指出，不稳定是由波纹界面上传播和反射的波纹激波留下的非均匀速度剪切所驱动的。在这项工作中，研究了非均匀涡旋片与密度跃迁的自相互作用时界面的非线性演化。发展的理论表明了有限密度跳跃和界面有限初始波纹幅度的重要性。通过在具有适当运动边界条件的界面上引入拉格朗日标记物，结果表明，即使在切向，界面也会局部发生伸缩。这会导致气泡和尖峰轮廓变形，具体取决于阿特伍德数。有限密度跃迁界面上的涡量在非线性区域是不守恒的。我们的结果表明，尖峰的螺旋结构是由于界面上涡量的局部增加和减少所致。非线性分析表明，波纹的大初始幅度导致涡量的快速增加，这也可以解释螺旋在大幅度时的快速卷起运动。利用渐近线性增长率，由界面的初始波纹幅度、阿特伍德数和入射激波强度唯一地确定了不稳定性的非线性演化。没有必要使用冲动的提法。解析的非线性增长与实验符合得很好[Dimonte等人，Phys.等离子体3,614(1996)]。该理论揭示了不稳定性的非线性特性，如界面轮廓和界面涡量的时间演化，以及它们对阿特伍德数和波纹幅度的依赖关系。
The linear theory of the Richtmyer-Meshkov instability derived by Wouchuk and Nishihara [Phys. Plasmas 4, 3761 (1997)] indicates that the instability is driven by the nonuniform velocity shear left by transmitted and reflected rippled shocks at a corrugated interface. In this work, the nonlinear evolution of the interface has been investigated as a self-interaction of a nonuniform vortex sheet with a density jump. The theory developed shows the importance of the finite density jump and the finite initial corrugation amplitude of the interface. By introducing Lagrangian markers on the interface with proper kinematic boundary conditions, it is shown that stretching and shrinking of the interface occur locally even in the tangential direction. This causes deformation of bubble and spike profiles depending on the Atwood number. The vorticity on the interface for a finite density jump is not conserved in the nonlinear regime. Our results suggest that the spiral structure of the spike is due to local increase and decrease of the vorticity on the interface. Nonlinear analysis shows that the large initial amplitude of the corrugation results in rapid increase of the vorticity, which may also explain the fast roll up motion of the spiral for large amplitudes. With the use of the asymptotic linear growth rate, the nonlinear evolution of the instability is uniquely determined from the initial corrugation amplitude of the interface, the Atwood number, and the incident shock intensity. There is no need to use an impulsive formulation. The analytical nonlinear growth agrees well with the experiment [Dimonte et al., Phys. Plasmas 3, 614 (1996)]. The theory reveals nonlinear properties of the instability, such as the time evolution of the interface profiles and the vorticity on the interface, and also their dependence on the Atwood number and the corrugation amplitude.