Vortex sheet motion in incompressible Richtmyer–Meshkov and Rayleigh–Taylor instabilities with surface tension
Vortex sheet motion in incompressible Richtmyer–Meshkov and Rayleigh–Taylor instabilities with surface tension
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具有表面张力的不可压缩 Richtmyer-Meshkov 和 Rayleigh-Taylor 不稳定性中的涡旋片运动
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
C. Matsuoka
中科院分区：
文献类型：
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作者：
C. Matsuoka
用边界积分方法数值研究了具有表面张力的不可压Richtmyer-Meshkov（RM）和Rayleigh-Taylor（RT）不稳定性中的平面界面运动。结果表明，当阿特伍德数是小的，界面卷起没有正则化的界面速度。在不同的阿特伍德数和表面张力系数的计算的最后阶段中观察到的现象被称为“捏”的物理滴，它表明，这种现象是由界面上诱导的涡旋偶极子。当表面张力系数较大时，RM不稳定性存在有限振幅驻波解。通过非线性稳定性分析，详细研究了驻波解。当考虑重力时（RT不稳定性），在系统中线性色散关系的频率等于零的临界条件下，可以发生线性稳定但非线性不稳定的运动。此外，它表明，在此临界运动下的气泡和尖峰的增长率既不是指数型，也不是幂律型在线性阶段和渐近阶段。
Motion of a planar interface in incompressible Richtmyer–Meshkov (RM) and Rayleigh–Taylor (RT) instabilities with surface tension is investigated numerically by using the boundary integral method. It is shown that when the Atwood number is small, an interface rolls up without regularization of the interfacial velocity. A phenomenon known as “pinching” in the physics of drops is observed in the final stage of calculations at various Atwood numbers and surface tension coefficients, and it is shown that this phenomenon is caused by a vortex dipole induced on the interface. It is also shown that when the surface tension coefficient is large, finite amplitude standing wave solutions exist for the RM instability. This standing wave solution is investigated in detail by nonlinear stability analysis. When gravity is taken into account (RT instability), linearly stable but nonlinearly unstable motion can occur under a critical condition that the frequency of the linear dispersion relation in the system is equal to zero. Further, it is shown that the growth rate of bubbles and spikes under this critical motion is neither of the exponential type nor of the power law type at both the linear stage and the asymptotic stage.