The interaction of rarefaction waves and a heavy/light interface is investigated using numerical simulations by solving the compressible Euler equations. An upwind space–time conservation element and solution element (CE/SE) scheme with second-order accuracy in both space and time is adopted. Rarefaction waves are generated by simulating the shock-tube problem. In this work, the SF6/air interface evolution under different conditions is considered. First, the gas physical parameters before and after the rarefaction waves impact the interface are calculated using one-dimensional gas dynamics theory. Then, the interaction between the rarefaction waves and a single-mode perturbation interface is investigated, and both the interface evolution and the wave patterns are obtained. Afterwards, the amplitude growth of the interface over time is compared between cases, considering the effects of the interaction period and the strength of the rarefaction waves. During the interaction of the rarefaction waves with the interface, the Rayleigh–Taylor instability induced by the rarefaction waves is well predicted by modifying the nonlinear model proposed by Zhang & Guo (J. Fluid Mech., vol. 786, 2016, pp. 47–61), considering the variable acceleration. After the rarefaction waves leave the interface, the equivalent Richtmyer–Meshkov instability is well depicted by the nonlinear model proposed by Zhang et al. (Phys. Rev. Lett., vol. 121(17), 2018, 174502), considering the growth rate transition from Rayleigh–Taylor instability to Richtmyer–Meshkov instability. The differences in the heavy/light interface amplitude growth under the rarefaction wave condition and the shock wave condition are compared. The interface perturbation is shown to be more unstable under rarefaction waves than under a shock wave.

中文翻译：

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稀薄波引起的重/轻界面的界面不稳定性

通过求解可压缩欧拉方程，使用数值模拟研究稀疏波和重/轻界面的相互作用。采用在空间和时间上均具有二阶精度的逆风时空守恒元和解元（CE/SE）方案。稀薄波是通过模拟激波管问题产生的。在这项工作中，考虑了不同条件下 SF6/空气界面的演变。首先，利用一维气体动力学理论计算了稀疏波冲击界面前后的气体物理参数。然后，研究了稀疏波与单模微扰界面之间的相互作用，并获得了界面演化和波型。然后，考虑到相互作用周期和稀疏波强度的影响，比较了不同情况下界面随时间的振幅增长。在稀疏波与界面的相互作用过程中，通过修改 Zhang & Guo 提出的非线性模型，可以很好地预测由稀疏波引起的 Rayleigh-Taylor 不稳定性（J. Fluid Mech., vol. 786, 2016, pp. 47 –61)，考虑可变加速度。在稀疏波离开界面后，Zhang 等人提出的非线性模型很好地描述了等效的 Richtmyer-Meshkov 不稳定性。(Phys. Rev. Lett., vol. 121(17), 2018, 174502)，考虑到增长率从瑞利-泰勒不稳定性到里奇迈尔-梅斯科夫不稳定性的转变。比较了稀疏波条件和冲击波条件下重/轻界面振幅增长的差异。界面扰动在稀疏波下比在冲击波下更不稳定。