B322 リヒトマイヤー・メシュコフ不安定性における境界面の時間発展

概要

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The nonlinear evolution of an interface in Richtmyer-Meshkov (R-M) instability is investegeted. The difference between Kelvin-Helmholtz or Rayleigh-Taylor instability and R-M instability consists in whether the sound wave exists or not. In order to describe the flow field, we adopt the wave equation instead of Laplace equation, which has been used to analyse R-M instability by a lot of researchers. If we assume the similarity solution to the wave equation, we can obtain Laplace equation described by similarity variables. This assumption means that the flow field described by the similarity variables can be considered as imcompressive. We show that it is essential in R-M instability to exist the sound wave, and the self-similar solution of the wave equation enables us to caluculate the higher order terms in the perturbation expansions without the appearance of secular terms. We obtain the result that all sinusoidal modes of the amplitude of the interface grow with time t, while the nonlinear interaction terms decrease with t^<-1>.
日本流体力学会の論文
2000-07-25