Numerical study of shock-induced Richtmyer-Meshkov instability in inhomogeneous heavy fluid layer

The shock-induced Richtmyer-Meshkov instability in an inhomogeneous semi-infinite or finite thickness heavy fluid layer is numerically investigated to study the influences of the fluid layer and inhomogeneity on the interface evolution. The initial planar shock wave first propagates in an inhomogeneous light gas, which becomes curved and then interacts with an inhomogeneous heavy fluid layer. The density of the light and heavy fluid is set to a cosine-function distribution along the transverse direction to mimic an inhomogeneous fluid. When the density variation is in-phase in the light and heavy fluid, compared with the semi-infinite layer case, the Kelvin-Helmholtz instability is more pronounced and the amplitude grows faster in the finite thickness fluid layer. The heavy fluid layer is stretched in the flow direction with a larger amplitude. When the density variation is anti-phase, phase reversion occurs for the curved transited shock wave passing through the two interfaces, which induces a totally different evolution of the interface structure that the heavy fluid layer is flat and coarse with a significant jet structure and the amplitude growth was reduced. An efficient prediction model is improved for the development of the interface amplitude in the presence of inhomogeneities in the light gas and heavy fluid layer.