Turbulent mixing and transition criteria of flows induced by hydrodynamic instabilities

Abstract

In diverse areas of science and technology, including inertial confinement fusion (ICF), astrophysics, geophysics, and engineering processes, turbulent mixing induced by hydrodynamic instabilities is of scientific interest as well as practical significance. Because of the fundamental roles they often play in ICF and other applications, three classes of hydrodynamic instability-induced turbulent flows—those arising from the Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz instabilities—have attracted much attention. ICF implosions, supernova explosions, and other applications illustrate that these phases of instability growth do not occur in isolation, but instead are connected so that growth in one phase feeds through to initiate growth in a later phase. Essentially, a description of these flows must encompass both the temporal and spatial evolution of the flows from their inception. Hydrodynamic instability will usually start from potentially infinitesimal spatial perturbations, will eventually transition to a turbulent flow, and then will reach a final state of a true multiscale problem. Indeed, this change in the spatial scales can be vast, with hydrodynamic instability evolving from just a few microns to thousands of kilometers in geophysical or astrophysical problems. These instabilities will evolve through different stages before transitioning to turbulence, experiencing linear, weakly, and highly nonlinear states. The challenges confronted by researchers are enormous. The inherent difficulties include characterizing the initial conditions of such flows and accurately predicting the transitional flows. Of course, fully developed turbulence, a focus of many studies because of its major impact on the mixing process, is a notoriously difficult problem in its own right. In this pedagogical review, we will survey challenges and progress, and also discuss outstanding issues and future directions.

Early Time Modifications to the Buoyancy-Drag Model for Richtmyer–Meshkov Mixing

“…It is apparent from these review papers that both RM and RT are strongly influenced by the initial conditions and this needs to be taken into account if any form of engineering modelling is used. The analysis given in this paper describes, for a particular case, a way of modelling the transition to turbulence, an issue of significant current interest according to Zhou et al [21].…”

Self-similar solutions of asymmetric Rayleigh-Taylor mixing

“…In general, the equations presented in the previous paragraph are used to determine its value, but there are a range of methods that have been applied in the literature 12 . Values of ∼ 0.05 found in experiments 12,14 , but values of 0.027 are found in 3D numerical simulations 9,12,15,16 . The initial spectrum of the perturbations can have a huge influence on the value of α obtained, with a difference of a factor of 2 to 3 11,17 as a result of the initial spectrum.…”

“…At late times this just reduces the model that comes from dimensional analysis 7 . As the late time limit is hard to achieve 9 , calculations of α using this method can depend heavily on the determination of the virtual origin, i.e. calculation h 0 .…”

“…The value of α has been the subject of much study [9][10][11][12][13] . In general, the equations presented in the previous paragraph are used to determine its value, but there are a range of methods that have been applied in the literature 12 .…”

“…This difference may be attributed to the importance of mass diffusion in different cases. For an overall review, see Zhou et al 9 .…”