High-fidelity experiments of Richtmyer–Meshkov instability on a single-mode air/$\text{SF}_{6}$ interface are carried out at weak shock conditions. The soap-film technique is extended to create single-mode gaseous interfaces which are free of small-wavelength perturbations, diffusion layers and three-dimensionality. The interfacial morphologies captured show that the instability evolution evidently involves the smallest experimental uncertainty among all existing results. The performances of the impulsive model and other nonlinear models are thoroughly examined through temporal variations of the perturbation amplitude. The individual growth of bubbles or spikes demonstrates that all nonlinear models can provide a reliable forecast of bubble development, but only the model of Zhang & Guo (J. Fluid Mech., vol. 786, 2016, pp. 47–61) can reasonably predict spike development. The distinct images of the interface morphology obtained also provide a rare opportunity to extract interface contours such that a spectral analysis of the interfacial contours can be performed, which realizes the first direct validation of the high-order nonlinear models of Zhang & Sohn (Phys. Fluids, vol. 9, 1997, pp. 1106–1124) and Vandenboomgaerde et al. (Phys. Fluids, vol. 14 (3), 2002, pp. 1111–1122) in terms of the fundamental mode and high-order harmonics. It is found that both models show a very good and almost identical accuracy in predicting the first two modes. However, the model of Zhang & Sohn (1997) becomes much more accurate in modelling the third-order harmonics due to the fewer simplifications used.

We report the first measurements of the perturbation amplitude in the converging Richtmyer-Meshkov instability in a semiannular shock tube. At early stages, the amplitude growth agrees well with the impulsive model considering the geometrical convergence effect. A quick decrease of the growth rate at late time, even to be negative, before the reshock is observed for the first time. The reduction of the growth rate is ascribed to the Rayleigh-Taylor stabilization caused by the interface deceleration motion only presented in the converging circumstance. By reasonably evaluating the Rayleigh-Taylor stabilization, a modified model based on the Bell equation is proposed, which well predicts the perturbation growth in a converging geometry from early to late stages before the reshock. It is also found that the flow compressibility is significant in the converging Richtmyer-Meshkov instability.

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.

The Richtmyer–Meshkov instability on a three-dimensional single-mode light/heavy interface is experimentally studied in a converging shock tube. The converging shock tube has a slender test section so that the non-uniform feature of the shocked flow is amply exhibited in a long testing time. A deceleration phenomenon is evident in the unperturbed interface subjected to a converging shock. The single-mode interface presents three-dimensional characteristics because of its minimum surface feature, which leads to the stratified evolution of the shocked interface. For the symmetry interface, it is quantitatively found that the perturbation amplitude experiences a rapid growth to a maximum value after shock compression and finally drops quickly before the reshock. This quick reduction of the interface amplitude is ascribed to a significant Rayleigh–Taylor stabilization effect caused by the deceleration of the light/heavy interface. The long-term effect of the Rayleigh–Taylor stabilization even leads to a phase inversion on the interface before the reshock when the initial interface has sufficiently small perturbations. It is also found that the amplitude growth is strongly suppressed by the three-dimensional effect, which facilitates the occurrence of the phase inversion.

The evolution of an $\text{SF}_{6}$ layer surrounded by air is experimentally studied in a semi-annular convergent shock tube by high-speed schlieren photography. The gas layer with a sinusoidal outer interface and a circular inner interface is realized by the soap-film technique such that the initial condition is well controlled. Results show that the thicker the gas layer, the weaker the interface–coupling effect and the slower the evolution of the outer interface. Induced by the distorted transmitted shock and the interface coupling, the inner interface exhibits a slow perturbation growth which can be largely suppressed by reducing the layer thickness. After the reshock, the inner perturbation increases linearly at a growth rate independent of the initial layer thickness as well as of the outer perturbation amplitude and wavelength, and the growth rate can be well predicted by the model of Mikaelian (Physica D, vol. 36, 1989, pp. 343–357) with an empirical coefficient of 0.31. After the linear stage, the growth rate decreases continuously, and finally the perturbation freezes at a constant amplitude caused by the successive stagnation of spikes and bubbles. The convergent geometry constraint as well as the very weak compressibility at late stages are responsible for this instability freeze-out.

Ritchmyer–Meshkov instability on an air/SF$_{6}$ interface is experimentally studied in a coaxial converging shock tube by a high-speed laser sheet imaging technique. An unperturbed case is first examined to obtain the characteristics of the converging shock and the shocked interface. For sinusoidal interfaces, the wave pattern and the interface morphology of the whole process are clearly observed. It is quantitatively found that the perturbation amplitude first decreases due to the shock compression, then experiences a rapid growth to a maximum value and finally drops quickly before the reshock. The reduction of growth rate is ascribed to the Rayleigh–Taylor stabilization caused by the interface deceleration motion that is present in the converging circumstance. It is noted that the influence of the wavenumber on the amplitude growth is very little before the reshock, but becomes significant after the reshock.

Abstract

A novel shock tube is designed to investigate the nonlinear feature of convergent Richtmyer–Meshkov instability on a single-mode interface formed by a soap film technique. The shock tube employs a concave–oblique–convex wall profile which first transforms a planar shock into a cylindrical arc, then gradually strengthens the cylindrical shock along the oblique wall, and finally converts it back into a planar one. Therefore, the new facility can realize analysis on compressibility and nonlinearity of convergent Richtmyer–Meshkov instability by eliminating the interface deceleration and reshock. Five sinusoidal $\text{air}{-}\text{SF}_{6}$ interfaces with different amplitudes and wavelengths are considered. For all cases, the perturbation amplitude experiences a linear growth much longer than that in the planar geometry. A compressible linear model is derived by considering a constant uniform fluid compression, which shows a slight difference to the incompressible theory. However, both the linear models overestimate the perturbation growth from a very early stage due to the presence of strong nonlinearity. The nonlinear model of Wang et al. (Phys. Plasmas, vol. 22, 2015, 082702) is demonstrated to predict well the amplitude growth up to a normalized time of 1.0. The prolongation of the linear increment is mainly ascribed to the counteraction between the promotion by geometric convergence and the suppression by nonlinearity. Growths of the first three harmonics, obtained by a Fourier analysis of the interface contour, provide a first thorough validation of the nonlinear theory.