Universal perturbation growth of Richtmyer–Meshkov instability for minimum-surface featured interface induced by weak shock waves

Abstract

Experimental and theoretical investigations are performed to explore the development of Richtmyer–Meshkov (RM) instability for a minimum-surface featured (3D-) interface. The exact mathematical expression of 3D-interface perturbation is obtained for the first time by the spectrum analysis, describing as a superposition of transverse two-dimensional (2D) single-mode with three-dimensional (3D) multi-mode. In particular, the normalized 3D-interface profile is found to be solely determined by one dimensionless parameter related to the 3D-interface initial spectrum. The shock tube experiments are performed by varying the interface height to change the mode-composition of 3D-interfaces under weak shock conditions. It is found that the 3D multi-mode component of a 3D-interface promotes/suppresses the RM instability at the transverse boundary/symmetry plane in comparison with the classical 2D single-mode case. At the linear regime, the 3D perturbation growth can be well predicted by combining the amplitude growth of a 2D single-mode and a 3D dual-mode. At the nonlinear regime, as the interface height reduces, the nonlinear effect on the RM instability at the boundary plane becomes stronger. A generalized nonlinear model is established to predict the interface amplitude by considering the interface spectrum and the mode-coupling of 3D modes. It is found that the mode-coupling has an evident influence on the bubble evolution, and the first-order 3D mode leads to different behaviors for the bubble and spike width growths. This work may provide great insight into the physical mechanism of the 3D RM instability existing in practical applications.