SIAM Journal on Applied Mathematics, Volume 81, Issue 3, Page 1002-1019, January 2021.
Rayleigh--Taylor (RT) and Richtmyer--Meshkov (RM) instabilities and RT/RM interfacial mixing are omnipresent in nature and technology and are often driven by variable acceleration. This work presents the detailed study of RT/RM dynamics induced by the acceleration varying as power-law with the length scale. We consider RT/RM dynamics within the framework of group theory and momentum model and find solutions for the scale-dependent dynamics and for the self-similar mixing. The effect of fluctuations on the self-similar mixing is also investigated by augmenting the momentum model with stochastic process. We find that the scale-dependent dynamics and the self-similar mixing can be RT type and RM type depending on the exponent of the acceleration power-law. For the scale-dependent dynamics the exponent value separating RT and RM subregimes approaches negative infinity, whereas for the self-similar mixing it is a finite negative value depending on the drag. Based on these results, we elaborate new theory benchmarks for future research.

中文翻译：

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尺度相关和自相似瑞利--Taylor and Richtmyer--加速度随长度尺度变化引起的Meshkov动力学

SIAM 应用数学杂志，第 81 卷，第 3 期，第 1002-1019 页，2021 年 1 月。
Rayleigh-Taylor (RT) 和 Richtmyer-Meshkov (RM) 不稳定性和 RT/RM 界面混合在自然界和技术中无处不在，通常由可变加速度驱动。这项工作详细研究了由加速度随长度尺度呈幂律变化而引起的 RT/RM 动力学。我们在群论和动量模型的框架内考虑 RT/RM 动力学，并为依赖于尺度的动力学和自相似混合找到解决方案。还通过用随机过程增强动量模型来研究波动对自相似混合的影响。我们发现依赖于尺度的动力学和自相似混合可以是 RT 型和 RM 型，这取决于加速度幂律的指数。对于与尺度相关的动力学，分离 RT 和 RM 子区域的指数值接近负无穷大，而对于自相​​似混合，它是取决于阻力的有限负值。基于这些结果，我们为未来的研究制定了新的理论基准。