Richtmyer-Meshkov instability (RMI) plays an important role in many areas of science and engineering, from supernovae and fusion to scramjets and nano-fabrication. Classical Richtmyer-Meshkov instability is induced by a steady shock and impulsive acceleration, whereas in realistic environments the acceleration is usually variable. We focus on RMI induced by acceleration with power-law time-dependence and apply group theory to solve the long-standing problem. For early-time dynamics, we find the dependence of the growth-rate on the initial conditions and show that it is independent of the acceleration parameters. For late-time dynamics, we find a continuous family of regular asymptotic solutions, including their curvature, velocity, Fourier amplitudes, and interfacial shear, and we study their stability. For each solution, the interface dynamics is directly linked to the interfacial shear, the non-equilibrium velocity field has intense fluid motion near the interface and effectively no motion in the bulk. The quasi-invariance of the fastest stable solution suggests that nonlinear coherent dynamics in RMI is characterized by two macroscopic length-scales -- the wavelength and the amplitude, in agreement with observations. The properties of a number of special solutions are outlined, these being respectively, the Atwood, Taylor, convergence, minimum-shear, and critical bubbles, among others. We also elaborate new theory benchmarks for future experiments and simulations.

中文翻译：

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具有时变加速度的不稳定三维界面相干结构中 Richtmyer-Meshkov 气泡的动力学

Richtmyer-Meshkov 不稳定性 (RMI) 在科学和工程的许多领域都发挥着重要作用，从超新星和聚变到超燃冲压发动机和纳米制造。经典的 Richtmyer-Meshkov 不稳定性是由稳定的冲击和脉冲加速度引起的，而在现实环境中，加速度通常是可变的。我们专注于由具有幂律时间依赖性的加速度引起的 RMI，并应用群论来解决长期存在的问题。对于早期动力学，我们发现了增长率对初始条件的依赖性，并表明它与加速度参数无关。对于后期动力学，我们找到了一系列连续的规则渐近解，包括它们的曲率、速度、傅立叶振幅和界面剪切，我们研究了它们的稳定性。对于每个解决方案，界面动力学与界面剪切直接相关，非平衡速度场在界面附近有强烈的流体运动，并且实际上没有运动。最快稳定解的准不变性表明 RMI 中的非线性相干动力学具有两个宏观长度尺度——波长和幅度，与观察结果一致。概述了许多特殊解的性质，它们分别是 Atwood、Taylor、收敛、最小剪切和临界气泡等。我们还为未来的实验和模拟制定了新的理论基准。最快稳定解的准不变性表明 RMI 中的非线性相干动力学具有两个宏观长度尺度——波长和幅度，与观察结果一致。概述了许多特殊解的性质，它们分别是 Atwood、Taylor、收敛、最小剪切和临界气泡等。我们还为未来的实验和模拟制定了新的理论基准。最快稳定解的准不变性表明 RMI 中的非线性相干动力学具有两个宏观长度尺度——波长和幅度，与观察结果一致。概述了许多特殊解的性质，它们分别是 Atwood、Taylor、收敛、最小剪切和临界气泡等。我们还为未来的实验和模拟制定了新的理论基准。