Analytical theory for Richtmyer-Meshkov instability in compressible fluids
数学专题报告
报告题目(Title)：Analytical theory for Richtmyer-Meshkov instability in compressible fluids
报告人(Speaker)：张强 (北京师范大学数学研究中心(珠海))
地点(Place)：后主楼1124
时间(Time)：2023年4月10日(周一), 10:30-11:30
邀请人(Inviter)：许孝精
报告摘要
Richtmyer-Meshkov instability is a classical problem in fluid dynamics originated from the path-breaking work of Richtmyer in 1960. Such an instability in compressible fluids is a very complicated phenomenon. Unstable fingers, known as spikes and bubbles, develop at the material interface between two fluids of different densities. A spike is the portion of the heavy fluid penetrating into the light fluid, and a bubble is the portion of the light fluid penetrating into the heavy fluid. It is very difficult to derive accurate theories to predict the growth rates of spikes and bubbles at the unstable material interface between compressible fluids. This is due to the facts that the fluids are compressible, the material interface is unstable, and the dynamics of the material interface is nonlinear. Theoretical studies usually approximate the fluids as incompressible and the incident shock as an impulsive force, and numerical simulations have been the main tools for studying the finger growth in Richtmyer-Meshkov instability in compressible fluids. In this talk, we present a new close-form approximate solution for the growth rate of fingers of Richtmyer-Meshkov instability in compressible fluids. Our theoretical approach consists of analyzing the dynamics of the unstable material interface, deriving closed-form solutions at early and late times, and applying asymptotic matching. Our theory contains no fitting parameters and is applicable to both spikes and bubbles, to compressible fluids, to systems with arbitrary density ratios, to incident shocks with arbitrary strength, and to the entire evolution process from early to late times. The theoretical predictions are in remarkably good agreements with the results from numerical simulations and the data from experiments. Even for a compressible fluid system with a Mach number of the incident shock being as high as 15.3, our theoretical predictions are still in an excellent agreement with the data from the numerical simulations.
