Convergent Richtmyer-Meshkov instability on two-dimensional tri-mode interfaces

Interfacial fluid mixing driven by a shock wave is a common phenomenon that occurs frequently in basic science research and in a variety of applications. In this work, shock-tube experiments on the developments of two-dimensional tri-mode interfaces accelerated by a convergent shock wave are performed. Eight sets of different combinations in the value of phase and that of amplitude in a tri-mode perturbed interface are studied to evaluate the effect of mode coupling on the amplitude growths of the basic modes. The qualitative results show that the phase combination obviously affects the interface morphologies and flow features. The alternation of each mode amplitude does not affect the major flow features, such as the number and arrangement of the bubbles and spikes, but affects the local interface features. Depending upon the phase combination, the mode amplitude growth is either promoted or suppressed by mode coupling relative to the single-mode counterpart. By considering the feedbacks from both the first-order and second-order mode couplings, the mode amplitude growth can be qualitatively predicted. Relative to dual-mode interface, mode coupling occurs earlier in tri-mode interface. For the sets of parameters we studied, the effect of initial phase on the amplitude growth is greater and occurs earlier for the mode with low mode number. In addition, the amplitude development of mode with high mode number is more affected by initial amplitudes of basic modes than that of mode with low mode number. The introduction of the third mode affects the amplitude growths of original two modes, but has little effect on the final mixing width growth. Finally, a theoretical model is proposed to predict the amplitude growth of each basic mode.