Richtmyer–Meshkov instability on a quasi-single-mode interface

Abstract

Experiments on Richtmyer–Meshkov instability of quasi-single-mode interfaces are performed. Four quasi-single-mode air/$\text{SF}_{6}$ interfaces with different deviations from the single-mode one are generated by the soap film technique to evaluate the effects of high-order modes on amplitude growth in the linear and weakly nonlinear stages. For each case, two different initial amplitudes are considered to highlight the high-amplitude effect. For the single-mode and saw-tooth interfaces with high initial amplitude, a cavity is observed at the spike head, providing experimental evidence for the previous numerical results for the first time. For the quasi-single-mode interfaces, the fundamental mode is the dominant one such that it determines the amplitude linear growth, and subsequently the impulsive theory gives a reasonable prediction of the experiments by introducing a reduction factor. The discrepancy in linear growth rates between the experiment and the prediction is amplified as the quasi-single-mode interface deviates more severely from the single-mode one. In the weakly nonlinear stage, the nonlinear model valid for a single-mode interface with small amplitude loses efficacy, which indicates that the effects of high-order modes on amplitude growth must be considered. For the saw-tooth interface with small amplitude, the amplitudes of the first three harmonics are extracted from the experiment and compared with the previous theory. The comparison proves that each initial mode develops independently in the linear and weakly nonlinear stages. A nonlinear model proposed by Zhang & Guo (J. Fluid Mech., vol. 786, 2016, pp. 47–61) is then modified by considering the effects of high-order modes. The modified model is proved to be valid in the weakly nonlinear stage even for the cases with high initial amplitude. More high-order modes are needed to match the experiment for the interfaces with a more severe deviation from the single-mode one.

Richtmyer–Meshkov instability on a dual-mode interface

“…The mode coupling in the dual-mode RMI with two basic waves of equivalent amplitudes acts earlier and more evidently than that of the multi-mode RMI with an initial dominant mode (Liang et al. 2019). The mode coupling process revealed in the dual-mode RMI would be of great use for understanding and modelling the multi-mode RMI.…”

“…Further, we performed experiments on quasi-single-mode interfaces formed by the same soap-film technique (Liang et al. 2019). It was found that the fundamental mode dominates the initial quasi-single-mode interface and, consequently, the effect of high-order modes on the amplitude growth can be ignored in the linear stage.…”

Mechanism and modelling of the secondary baroclinic vorticity in the Richtmyer–Meshkov instability

“…It is noted that, although can be approximated using the impulsive model of Richtmyer (1960), the reduction factor in this model can vary significantly with different initial conditions (see Liang et al. 2019).…”

“…(2009) and experimental data of Jacobs & Krivets (2005) and Liang et al. (2019) with key parameters summarized in table 4.…”

Advances in interfacial instability induced by reshock

“…激波诱导界面不稳定性, 又称为激波与界面相互 作用或Richtmyer-Meshkov (RM)不稳定性, 最早是由 Richtmyer [1] 在1960年做出理论预测, 并由Meshkov [2] [3] 、航天火箭发动机 [4] 、天体物理 [5] 等领域有着重要的研究和应用价值. 如, 它是惯性约束 [6][7][8][9][10][11][12][13][14][15][16][17][18][19] , 我国 学者也开展了丰富的研究工作并取得一系列重要进 展 [20][21][22][23][24][25][26][27][28][29] . 近年来, 相关的专题综述已经4次在Annual Review of Fluid Mechanics上发表 [30][31][32][33] .…”