Hydrodynamic instabilities such as Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities usually appear in conjunction with the Kelvin–Helmholtz (KH) instability and are found in many natural phenomena and engineering applications. They frequently result in turbulent mixing, which has a major impact on the overall flow development and other effective material properties. This can either be a desired outcome, an unwelcome side effect, or just an unavoidable consequence, but must in all cases be characterized in any model. The RT instability occurs at an interface between different fluids, when the light fluid is accelerated into the heavy. The RM instability may be considered a special case of the RT instability, when the acceleration provided is impulsive in nature such as that resulting from a shock wave. In this pedagogical review, we provide an extensive survey of the applications and examples where such instabilities play a central role. First, fundamental aspects of the instabilities are reviewed including the underlying flow physics at different stages of development, followed by an overview of analytical models describing the linear, nonlinear and fully turbulent stages. RT and RM instabilities pose special challenges to numerical modeling, due to the requirement that the sharp interface separating the fluids be captured with fidelity. These challenges are discussed at length here, followed by a summary of the significant progress in recent years in addressing them. Examples of the pivotal roles played by the instabilities in applications are given in the context of solar prominences, ionospheric flows in space, supernovae, inertial fusion and pulsed-power experiments, pulsed detonation engines and Scramjets. Progress in our understanding of special cases of RT/RM instabilities is reviewed, including the effects of material strength, chemical reactions, magnetic fields, as well as the roles the instabilities play in ejecta formation and transport, and explosively expanding flows. The article is addressed to a broad audience, but with particular attention to graduate students and researchers who are interested in the state-of-the-art in our understanding of the instabilities and the unique issues they present in the applications in which they are prominent.

诸如Rayleigh–Taylor（RT）和Richtmyer–Meshkov（RM）等流体力学不稳定性通常与Kelvin–Helmholtz（KH）不稳定性同时出现，并在许多自然现象和工程应用中发现。它们经常导致湍流混合，这对整体流动的发展和其他有效的材料性能产生重大影响。这可以是期望的结果，不受欢迎的副作用，也可以是不可避免的结果，但在任何情况下都必须在任何模型中进行特征化。当轻质流体加速进入重质流体时，RT不稳定性发生在不同流体之间的界面处。当所提供的加速度本质上是脉冲性的（例如由冲击波引起的加速度）时，RM不稳定性可被视为RT不稳定性的特殊情况。在此教学法评论中，我们对不稳定性起主要作用的应用和示例进行了广泛的调查。首先，对不稳定性的基本方面进行了回顾，包括在不同开发阶段的潜在流动物理学，然后概述了描述线性，非线性和完全湍动阶段的分析模型。RT和RM的不稳定性给数值建模带来了特殊的挑战，这是因为要求以逼真的方式捕获分离流体的尖锐界面。这些挑战在这里进行了详尽的讨论，然后总结了近年来在应对这些挑战方面取得的重大进展。在太阳突出，空间电离层流，超新星，惯性聚变和脉冲功率实验等背景下，给出了由不稳定性在应用中扮演的关键角色的示例，脉冲爆震发动机和超燃冲压发动机。综述了我们对RT / RM不稳定性特殊情况的理解进展，包括材料强度，化学反应，磁场的影响，以及不稳定性在喷射形成和运输以及爆炸性流动中所起的作用。本文面向的是广泛的读者，但特别关注那些对最新技术感兴趣的研究生和研究人员，他们对我们对不稳定性及其在突出应用中所遇到的独特问题的理解感兴趣。以及不稳定因素在喷射形成和运输以及爆炸性爆炸流动中所扮演的角色。本文面向的是广泛的读者，但特别关注那些对最新技术感兴趣的研究生和研究人员，他们对我们对不稳定性及其在突出应用中所遇到的独特问题的理解感兴趣。以及不稳定因素在喷射形成和运输以及爆炸性爆炸流动中所扮演的角色。本文面向的是广泛的读者，但特别关注那些对最新技术感兴趣的研究生和研究人员，他们对我们对不稳定性及其在突出应用中所遇到的独特问题的理解感兴趣。