Soap Film Technique Research Articles

Experimental investigation of three-dimensional Rayleigh–Taylor instability of a gaseous interface

Validating the theoretical work on Rayleigh–Taylor instability (RTI) through experiments with an exceptionally clean and well-characterized initial condition has been a long-standing challenge. Experiments were conducted to study the three-dimensional RTI of an SF $_6$ –air interface at moderate Atwood numbers. A novel soap film technique was developed to create a discontinuous gaseous interface with controllable initial conditions. Spectrum analysis revealed that the initial perturbation of the soap film interface is half the size of an entire single-mode perturbation. The correlation between the initial interface perturbation and Atwood numbers was determined. Due to the steep and highly curved feature of the initial soap film interface, the early-time evolution of RTI exhibits significant nonlinearity. In the quasi-steady regime, various potential flow models accurately predict the late-time bubble velocities by considering the channel width as the perturbation wavelength. Differently, the late-time spike velocities are described by these potential flow models using the wavelength of the entire single-mode perturbation. These findings indicate that the bubble evolution is influenced primarily by the spatial constraint imposed by walls, while the spike evolution is influenced mainly by the initial curvature of the spike tip. Consequently, a recent potential flow model was adopted to describe the time-varying amplitude growth induced by RTI. Furthermore, the self-similar growth factors for bubbles and spikes were determined from experiments and compared with existing studies, revealing that a large amplitude in the initial soap film interface promotes the spike development.

Divergent Richtmyer–Meshkov instability on a heavy gas layer

Experiments on divergent Richtmyer–Meshkov (RM) instability at a heavy gas layer are performed in a specially designed shock tube. A novel soap-film technique is extended to generate gas layers with controllable thicknesses and shapes. An unperturbed gas layer is first examined and its two interfaces are found to move uniformly at the early stage and be decelerated later. A general one-dimensional theory applicable to an arbitrary-thickness layer is established, which gives a good prediction of the layer motion in divergent geometry. Then, six kinds of perturbed SF $_6$ layers with various thicknesses and shapes surrounded by air are examined. At the early stage, the amplitude growths of the inner interface for various-thickness layers collapse quite well and also can be predicted by the Bell model for cylindrical RM instability at a single interface, which indicates a negligible interface coupling effect. Later, a rarefaction wave accelerates the inner interface, causing a dramatic rise in the growth rate. It is found that a thicker gas layer will result in a larger extent that the rarefaction wave can promote the instability growth. A modified Bell model accounting for both Rayleigh–Taylor (RT) instability and interface stretching caused by a rarefaction wave is established, which well reproduces the quick instability growth. At late stages, reverberating waves inside the layer are negligibly weak such that the inner interface growth is dominated by RM instability and RT stability. The major factors driving the outer interface development are a compression wave and interface coupling. A new interface coupling phenomenon existing uniquely in divergent geometry caused by the gradual thinning of the gas layer is observed and also modelled.

High-amplitude effect on single-mode Richtmyer–Meshkov instability of a light–heavy interface

The high-amplitude effect on the Richtmyer–Meshkov instability flow characteristics is investigated by examining the interaction of a planar shock with a single-mode air–SF6 interface both experimentally and numerically. In our experiments, the soap–film technique is adopted to generate well-defined initial interfaces, and the shocked flows are recorded by high-speed schlieren photography. Numerical simulations are performed to highlight the effects of wave patterns on interface movements at the early stage. For cases with high initial amplitudes, a cavity is formed at each spike tip. The cavity formation is ascribed to the vorticity deposition on the slip lines resulting from the Mach reflection of the transmitted shock wave. A series of transverse shocks introduce the secondary compression effect, which changes the interface morphology and causes the failure of the impulsive model in predicting the amplitude linear growth rate. Those modified linear models considering a reduction factor are also found incapable of accurately predicting the linear growth rate. Moreover, a non-monotone dependence of linear growth rate on initial amplitude is observed. Although similar observations were reported in previous numerical simulations, they have never been reported in experiments before. According to the pressure and velocity distributions, the effects of shock–shock interaction on the movements of the interface peak and trough are demonstrated, and the mechanism of non-monotone dependence is discussed. The validity of the existing nonlinear model proposed for predicting the development of a single-mode interface is further tested. It is shown that the applicability of the model worsens as the initial amplitude or dimensionless time increases.

Passive and active control for flow over a cylinder using a slit and validation with soap film technique

The flow over a slitted (0.1D) cylinder is studied numerically and experimentally using CFD and soap-film at Re = 100 at varying slit angles (0°–90°). The numerical solution is obtained by solving the Unsteady Reynolds-Averaged-Navier–Stokes (URANS) equations, and coefficients of lift (CL) & drag (CD), velocity, and vorticity are analyzed. Experimentally, soap film is used to visually validate the scaler data of the flow pattern. It exploits the optical properties of soap film captured by a high-speed camera by the reflection of a monochromatic sodium lamp light. The passive control of the slit is observed at various slit angles that affects the lift and drag and injection and blowing/suction modes. The active control is carried out by oscillating a thin wall placed in the middle of the 90° slit with varying frequency and amplitude. The results show that passive slit does not change the overall flow pattern and with slight changes in the CL and average CD. However, greater influence occurs by actively changing the amplitude and frequency of the wall oscillation. The CL amplitude is increased with increasing frequency of wall oscillation, but the average CD only increased at the lock-in condition and slightly decreased at the other frequencies.

Effects of obstacles on shock-induced perturbation growth

Effects of obstacles on interface evolution and mixing width induced by Richtmyer–Meshkov instability are investigated experimentally and numerically. In the experiment, the soap film technique is adopted to create an initial interface whose shape is governed by constraint strips protruding into the flow field. By varying the heights of constraint strips protruding into the flow field, effects of obstacles on post-shock flow features are highlighted. First, the interaction of a planar shock with an unperturbed interface is investigated numerically and experimentally. The results show that the obstacles have negligible effects on the transmitted shock velocity, but they greatly increase the reflected shock velocity. The obstacles induce the non-uniform pressure and velocity fields behind the shock, which change the interface evolution and mixing width. Then, experiments of planar shock wave interacting with single-mode interfaces with different initial amplitudes are performed. Induced by the non-uniform post-shock flow, the experimental schlieren images indicate that the spike tip becomes flat, but its size increases in the spanwise direction and the volume of the bubble is reduced. The effects of obstacles are magnified as their heights increase and are more pronounced when the initial interface amplitudes are small. The linear and nonlinear growth rates obtained from experiments show that the obstacles inhibit the perturbation growth, which is partially caused by less kinetic energy the interface obtains from the shock due to the block by the obstacles.

Convergent Richtmyer–Meshkov instability on a light gas layer with perturbed inner and outer surfaces

The instability of an annular helium gas layer surrounded by air with sinusoidal inner and outer interfaces, formed by a novel soap-film technique, impacted by a cylindrically convergent shock is experimentally studied in a semi-annular shock tube. Detailed evolution of the interfaces and wave patterns is captured by a high-speed Schlieren system. The focus is placed on the influences of layer thickness and phase difference between the inner and outer interfaces on the instability development. It is found that the larger the layer thickness, the quicker the early stage development of the outer interface. This is because the layer thickness affects the arrival time of the reflected shock (RS) at the outer interface and further determines the direction of baroclinic vorticity deposited on the outer interface by RS; namely, RS inhibits or promotes the instability growth depending on the layer thickness. It is also found that phase difference between the inner and outer perturbations produces a negligible (an evident) influence on the early stage (late-stage) instability growth at the outer interface, whereas a considerable (weak) influence on the early stage (late-stage) instability growth at the inner interface. This finding suggests that the early stage development of the outer (inner) interface can be modulated by changing the layer thickness (perturbation phase difference). Empirical coefficient in the Charakhch'an model [J. Appl. Mech. 41, 23–31 (2000)] is calculated to be β=0.52 by comparing the prediction with the experimental results. The model with β=0.52 gives a reasonable prediction of the post-reshock growth rate for all the cases considered in this work.

Evolution of shock-accelerated double-layer gas cylinder

Developments of the shock-accelerated concentric double-layer gas cylinder with an air cylinder embedded into an SF6 cylinder have been experimentally investigated for the first time. The double-layer gas cylinder is created by the soap film technique. Effects of the inner cylinder on the evolution of the outer one are highlighted by changing the radius ratio, i.e., a ratio of the inner radius to the outer one. The flow features show that the two cylinders evolve independently at the early stage, whereas they couple together at the late stage. The presence of the inner cylinder changes the behavior of shock movements, and a vortex pair instead of an outward jet is generated at the downstream interface. The scale of the vortex pair is proportional to the initial radius ratio. The rarefaction waves generated from the upstream interface of the inner cylinder accelerate the upstream interface of the outer cylinder earlier than the single-layer SF6 cylinder. Depending on the radius ratio, the acceleration induced by the rarefaction wave impact either prolongs or shortens the linear phase of the upstream interface movement. The waves' effect results in the failure of the nonlinear model in predicting the upstream interface movement. For the outer cylinder, its movements in both the streamwise and spanwise directions are promoted by the inner one. For the inner cylinder, its movements in the streamwise and spanwise directions are, respectively, inhibited and promoted by the outer one. As the radius ratio increases, the effect of promotion or prohibition is stronger.

Effects of transverse shock waves on early evolution of multi-mode chevron interface

Effects of transverse shock waves are important in the evolution of a multi-mode interface. However, the related experimental studies are scarce due to the difficulty in creating a well-defined interface. In the present work, we realized such an experimental study by using the soap film technique to form a multi-mode chevron air/SF6 interface. By changing the shock Mach number and the initial amplitude of the interface, the intensity of the transverse shock waves is varied. It is found that the impact of transverse shock waves together with the shock proximity effects flattens the bubble front and reduces the amplitude growth rate. For small initial amplitudes where the transverse shock waves are weak enough, the interface deforms little and the mode coupling is proven to be weak. For high initial amplitudes, the inverse cascade of modes causes the amplitude increase (decrease) of the first mode (high-order modes) at low Mach numbers. As the Mach number increases, the transverse shock waves and the shock proximity effects introduce external forces to the flow, resulting in the generation of additional high-order modes and the reduction in the first mode amplitude. Specifically, the augment of the second harmonic mode amplitude is crucial to flattening the bubble front.

Study on Richtmyer-Meshkov instability at heavy/lightsingle-mode interface

The Richtmyer-Meshkov (RM) instability at a heavy/light single-mode interface is studied both experimentally and numerically in this work, focusing on the interface structure evolution and the perturbation amplitude growth. The difference between the RM instability of the heavy/light interface and the light/heavy case (J. Fluid Mech., 2018, 853: R2) is discussed. Experimentally, an advanced soap film technique is adopted to generate an SF6/air gaseous interface with a controllable shape such that the instability development can be accurately examined. Detailed evolutions of the interface morphology and the wave pattern are captured by a high-speed video camera combined with schlieren photography. It is observed that the interfacial morphology presents an evident stratification after the phase inversion of the interface (the bubble (spike) reverses to be a spike (bubble)), which is mainly ascribed to the droplet cloud produced by the rupture of the soap film impacted by an incident shock wave. Numerically, a high-order accurate solver for compressible multi-phase flow, which has been thoroughly validated in previous shock-interface interaction studies, is employed to simulate the present heavy/light RM instability. The numerical results show good agreements with the experimental ones, which enables us to perform a detailed flow analysis. Different from the light/heavy case, after the shock impact, the heavy/light interface immediately enters the phase reversal process. After the phase reversal, the interface experiences successively the linear and nonlinear growths, which is similar to the light/heavy case. The reliable experimental and numerical results here allow us to examine the validity of the previous linear and nonlinear models for the heavy/light RM instability growth. It is found that the linear model of Meyer & Blewett (Phys. Fluids, 1972, 15: 753–759) gives a good prediction of the perturbation growth at linear stage up to a dimensionless time of 0.7, and the empirical model of Dimonte & Ramaprabhu (Phys. Fluids, 2010, 22: 014104) reasonably predicts the perturbation growth at the nonlinear stage, which is different from the light/heavy case where the model of Zhang & Guo (J Fluid Mech., 2016, 786: 47–61) gives the best prediction as suggested by an elaborate experimental study. Our study may facilitate the thorough understanding of the heavy/light RM instability and also can serve as a benchmark for new models.

Evolution of shock-accelerated heavy gas layer

Richtmyer–Meshkov instability of the SF6 gas layer surrounded by air is experimentally investigated. Using the soap film technique, five kinds of gas layer with two sharp interfaces are generated such that the development of each individual interface is highlighted. The flow patterns are determined by the amplitudes and phases of two corrugated interfaces. For a layer with both interfaces planar, the interface velocity shows that the reflected rarefaction waves from the second interface accelerate the first interface motion. For a layer with the second interface corrugated but the first interface planar, the reflected rarefaction waves make the first interface develop with the same phase as the second interface. For a layer with the first interface corrugated but the second interface planar, the rippled shock seeded from the first interface makes the second interface develop with the same phase as the first interface and the layer evolves into an ‘upstream mushroom’ shape. For two interfaces corrugated with opposite (the same) phase but a larger amplitude for the first interface, the layer evolves into ‘sinuous’ shape (‘bow and arrow’ shape, which has never been observed previously). For the interface amplitude growth in the linear stage, the waves’ effects are considered in the model to give a better prediction. In the nonlinear stage, the effect of the rarefaction waves on the first interface evolution is quantitatively evaluated, and the nonlinear growth is well predicted. It is the first time in experiments to quantify the interfacial instability induced by the rarefaction waves inside the heavy gas layer.

Convergent Richtmyer–Meshkov instability of light gas layer with perturbed outer surface

The convergent Richtmyer–Meshkov instability (RMI) of an layer with a uniform outer surface and a sinusoidal inner surface surrounded by air (generated by a novel soap film technique) is studied in a semiannular convergent shock tube using high-speed schlieren photography. The outer interface initially suffers only a slight deformation over a long period of time, but distorts quickly at late stages when the inner interface is close to it and produces strong coupling effects. The development of the inner interface can be divided into three stages. At stage I, the interface amplitude first drops suddenly to a lower value due to shock compression, then decreases gradually to zero (phase reversal) and later increases sustainedly in the negative direction. After the reshock (stage II), the perturbation amplitude exhibits long-term quasi-linear growth with time. The quasi-linear growth rate depends weakly on the pre-reshock amplitude and wavelength, but strongly on the pre-reshock growth rate. An empirical model for the growth of convergent RMI under reshock is proposed, which reasonably predicts the present results and those in the literature. At stage III, the perturbation growth is promoted by the Rayleigh–Taylor instability caused by a rarefaction wave reflected from the outer interface. It is found that both the Rayleigh–Taylor effect and the interface coupling depend heavily on the layer thickness. Therefore, controlling the layer thickness is an effective way to modulate the late-stage instability growth, which may be useful for the target design.

Coupling effect on shocked double-gas cylinder evolution

Interaction of a weak planar shock wave with double heavy gas cylinders has been investigated, focusing on coupling effect on the post-shock flow. In experiments, the ideal two-dimensional discontinuous double heavy gas cylinders with controllable initial conditions are generated by soap film technique, and the shocked flow is captured by a high-speed schlieren photography. Two different initial center spacings of cylinders are considered to highlight the coupling effect. As the center spacing reduces, the coupling effect occurs earlier and becomes more prominent. The coupling effect greatly promotes the inner vortex motions near the symmetry axis relative to the outer ones, resulting in the formation of the mushroom and twisted jets. The fusion of the inner vortices completely differs from the observation in previous experimental work in which the inner vortices separate from each other. Quantitatively, the motion of the upstream interface in streamwise direction is obtained, and can be predicted by a nonlinear model considering the coupling effect. Besides, a vortex model is proposed based on the induction equation of point vortex, and the effect of the mutual interferences among vortices on the vortex motions can be well evaluated.

Convergent Richtmyer–Meshkov instability of a heavy gas layer with perturbed outer interface

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.

Nonlinear behaviour of convergent Richtmyer–Meshkov instability

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 Wanget 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.

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

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.

Effects of non-periodic portions of interface on Richtmyer–Meshkov instability

The development of a non-periodic $\text{air}\text{/}\text{SF}_{6}$ gaseous interface subjected to a planar shock wave is investigated experimentally and theoretically to evaluate the effects of the non-periodic portions of the interface on the Richtmyer–Meshkov instability. Experimentally, five kinds of discontinuous chevron-shaped interfaces with or without non-periodic portions are created by the extended soap film technique. The post-shock flows and the interface morphologies are captured by schlieren photography combined with a high-speed video camera. A periodic chevron-shaped interface, which is multi-modal (81 % fundamental mode and 19 % high-order modes), is first considered to evaluate the impulsive linear model and several typical nonlinear models. Then, the non-periodic chevron-shaped interfaces are investigated and the results show that the existence of non-periodic portions significantly changes the balanced position of the initial interface, and subsequently disables the nonlinear model which is applicable to the periodic chevron-shaped interface. A modified nonlinear model is proposed to consider the effects of the non-periodic portions. It turns out that the new model can predict the growth of the shocked non-periodic interface well. Finally, a method is established using spectrum analysis on the initial shape of the interface to separate its bubble structure and spike structure such that the new model can apply to any random perturbed interface. These findings can facilitate the understanding of the evolution of non-periodic interfaces which are more common in reality.

Effects of aspect ratio on shock-cylinder interaction

Interaction of a planar shock wave with a discontinuous \(\hbox {SF}_6\) elliptic gas cylinder surrounded by air is investigated. Special attention is given to the effects of aspect ratio on wave pattern, interface evolution, and material mixing. An ideal discontinuous two-dimensional gas cylinder is created by the soap film technique in experiments, and the shocked flow is captured by schlieren photography combined with a high-speed video camera. The surface of the gas cylinder is clear enough to observe the shock motions, and the distinct interface boundaries allow us to extract more details. As aspect ratio varies, the shock focusing process is quite different. For the prolate gas cylinder, an inward jet is produced although an internal shock focusing firstly occurs. The inward jet has never been observed in membraneless prolate ellipse experiments probably because the inward jet is so faint due to less vorticity generation on membraneless interface that it is difficult to be observed. For the oblate gas cylinder, a secondary vortex pair, which has not been described clearly in previous work, is derived from the downstream interface. The material lines at early stages are extracted from experiments, which grow faster as aspect ratio increases. The interfacial area, the mean volume fraction and the mixing rate are presented from computations, and the results show that the increase of aspect ratio promotes the mixing between gases.

Interaction of planar shock wave with three-dimensional heavy cylindrical bubble

Interactions of a planar shock wave with two-dimensional (2D), three-dimensional (3D) concave, and 3D convex SF6 cylindrical bubbles surrounded by air are studied both experimentally and numerically. The effects of initial interface curvature on the bubble deformation and wave propagation are highlighted. The cylindrical bubbles are generated by a wire-restriction method based on the soap-film technique, and their shapes are well controlled by adjusting the pressure difference across the interface. The high-speed schlieren results demonstrate that the evolving interfaces develop more symmetrically than previous studies as they are free of holder and fewer disturbance waves are generated. Typical evolution processes of the 2D bubble such as the jet formation and vortex pair formation are clearly captured. Compared with the 2D case, the oppositely (identically) signed principal curvatures of the concave (convex) boundary produce more complicated high pressure fields and 3D additional baroclinic vorticity. For 3D cases, the numerical results show that the wave patterns in the symmetry or boundary slice are distinct from the 2D case owing to the 3D movement of the generated waves, and the jet structure presents an evident three dimensionality. In particular, for the concave bubble, a certain slice between the boundary and symmetry slices presents the fastest-developing jet, while for the convex case the fastest jet emerges at the boundary slice. The upstream interface along the symmetry slice of the concave (convex) bubble moves faster (slower) than that of the 2D case, which is reasonably predicted by a 3D theoretical model.

An elaborate experiment on the single-mode Richtmyer–Meshkov instability

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.

Interaction of rippled shock wave with flat fast-slow interface

The evolution of a flat air/sulfur-hexafluoride interface subjected to a rippled shock wave is investigated. Experimentally, the rippled shock wave is produced by diffracting a planar shock wave around solid cylinder(s), and the effects of the cylinder number and the spacing between cylinders on the interface evolution are considered. The flat interface is created by a soap film technique. The postshock flow and the evolution of the shocked interface are captured by a schlieren technique combined with a high-speed video camera. Numerical simulations are performed to provide more details of flows. The wave patterns of a planar shock wave diffracting around one cylinder or two cylinders are studied. The shock stability problem is analytically discussed, and the effects of the spacing between cylinders on shock stability are highlighted. The relationship between the amplitudes of the rippled shock wave and the shocked interface is determined in the single cylinder case. Subsequently, the interface morphologies and growth rates under different cases are obtained. The results show that the shock-shock interactions caused by multiple cylinders have significant influence on the interface evolution. Finally, a modified impulsive theory is proposed to predict the perturbation growth when multiple solid cylinders are present.