Rayleigh-Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. I. (English) Zbl 1377.76016
Summary: Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities play an important role in a wide range of engineering, geophysical, and astrophysical flows. They represent a triggering event that, in many cases, leads to large-scale turbulent mixing. Much effort has been expended over the past 140 years, beginning with the seminal work of Lord Rayleigh, to predict the evolution of the instabilities and of the instability-induced mixing layers. The objective of Part I of this review is to provide the basic properties of the flow, turbulence, and mixing induced by RT, RM, and Kelvin-Helmholtz (KH) instabilities. Historical efforts to study these instabilities are briefly reviewed, and the significance of these instabilities is discussed for a variety of flows, particularly for astrophysical flows and for the case of inertial confinement fusion. Early experimental efforts are described, and analytical attempts to model the linear, and nonlinear regimes of these mixing layers are examined. These analytical efforts include models for both single-mode and multi-mode initial conditions, as well as multi-scale models to describe the evolution. Comparisons of these models and theories to experimental and simulation studies are then presented. Next, attention is paid to the issue of the influence of stabilizing mechanisms (e.g., viscosity, surface tension, and diffuse interface) on the evolution of these instabilities, as well as the limitations and successes of numerical methods. Efforts to study these instabilities and mixing layers using group-theoretic ideas, as well as more formal notions of turbulence cascade processes during the later stages of the induced mixing layers, are inspected. A key element of the review is the discussion of the late-time self-similar scaling for the RT and RM growth factors, \(\alpha\) and \(\theta\). These parameters are influenced by the initial conditions and much of the observed variation can be explained by this. In some cases, these instabilities induced flows can transition to turbulence. Both the spatial and temporal criteria to achieve the transition to turbulence have been examined. Finally, a description of the energy-containing scales in the mixing layers, including energy “injection” and cascade processes are presented in greater detail. Part II of this review is designed to provide a much broader and in-depth understanding of this critical area of research [the author, ibid. 723–725, 1–160 (2017; Zbl 1377.76017)].
MSC:
| 76E09 | Stability and instability of nonparallel flows in hydrodynamic stability |
| 76E15 | Absolute and convective instability and stability in hydrodynamic stability |
| 76E17 | Interfacial stability and instability in hydrodynamic stability |
| 82D10 | Statistical mechanics of plasmas |
| 76X05 | Ionized gas flow in electromagnetic fields; plasmic flow |
| 76F25 | Turbulent transport, mixing |
Keywords:
Rayleigh-Taylor instability; Richtmyer-Meshkov instability; Kelvin-Helmholtz instability; shock waves; transition; turbulence; mixing; astrophysical fluid dynamics; SuperNovae; inertial confinement fusion (ICF); high energy density physics (HEDP); direct numerical simulations (DNS); Large-eddy simulations (LES)Citations:
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