Attenuation and even freeze-out (amplitude growth stagnation) of the perturbation amplitude growth of a shocked SF$_6$–air interface are first realized in shock-tube experiments through reflected rarefaction waves, which produce reverse baroclinic vorticity offsetting the vorticity deposited by the shock. A theoretical model is constructed to predict the perturbation growth after the impact of rarefaction waves, and seven possibilities of amplitude growth are analysed. Experimentally, a planar air–helium interface is used to produce reflected rarefaction waves. Through changing the perturbation wavelength and the time interval of two impacts, five experiments with specific initial conditions are carried out, and three different possibilities of perturbation growth attenuation are realized.

The reshocked Richtmyer–Meshkov instability (RMI) is examined in three different configurations via shock-tube experiments: RMI at a single-mode interface with a planar reshock (configuration I); RMI at a flat interface with a sinusoidal reshock (configuration II); RMI at a single-mode interface with a sinusoidal reshock (configuration III). The sinusoidal reshock is created by an incident shock reflecting off a sine-shaped wall surface. For all three configurations, the initial conditions of the experiment are specially set such that the interface evolution is at the linear stage when the reshock arrives. It is found that the amplitude of the reshocked interface increases linearly with time for all three configurations. For configuration I, the post-reshock perturbation growth depends heavily on the pre-reshock amplitude and growth rate, which can be predicted by a modified Mikaelian model (Phys. Rev. A, vol. 31, 1985, pp. 410–419). For configuration II, velocity perturbation associated with the non-uniform rippled reshock plays an important role in the instability growth. For configuration III, the post-reshock instability growth is much quicker (lower) than in configuration I when the sinusoidal reshock is in phase (out of phase) with the interface. A major reason is that for the in-phase (anti-phase) case, the velocity perturbation gives rise to an instability growth with an identical (opposite) direction to the pressure perturbation. A linear theory is developed that takes velocity perturbation, pressure perturbation and pre-reshock growth rate into account, which gives a reasonable prediction of the growth of the reshocked RMI in configurations II and III.

We report the first shock-tube experiments on two-dimensional dual-mode air–SF$_6$ interfaces with different initial spectra subjected to a convergent shock wave. The convergent shock tube is specially designed with a tail opening to highlight the Bell–Plesset (BP) and mode-coupling effects on amplitude development of fundamental mode (FM). The results show that the BP effect promotes the occurrence of mode coupling, and the feedback of high-order modes to the FM also arises earlier in convergent geometry than that in its planar counterpart. Relatively, the amplitude growth of the FM with a higher mode number is inhibited by the feedback, and saturates earlier. The FM with a lower mode number is affected more heavily by the BP effect, and finally dominates the flow. A new model is proposed to well predict the amplitude growths of the FM and high-order modes in convergent geometry. In particular, for FM that reaches its saturation amplitude, the post-saturation relation is introduced in the model to achieve a better prediction.

Shock-tube experiments are performed on the convergent Richtmyer–Meshkov (RM) instability of a multimode interface. The temporal growth of each Fourier mode perturbation is measured. The hydrodynamic instabilities, including the RM instability and the additional Rayleigh–Taylor (RT) effect, imposed by the convergent shock wave on the dual-mode interface, are investigated. The mode-coupling effect on the convergent RM instability coupled with the RT effect is quantified. It is evident that the amplitude growths of all first-order modes and second-order harmonics and their couplings depend on the variance of the interface radius, and are influenced by the mode-coupling from the very beginning. It is confirmed that the mode-coupling mechanism is closely related to the initial spectrum, including azimuthal wavenumbers, relative phases and initial amplitudes of the constituent modes. Different from the conclusion in previous studies on the convergent single-mode RM instability that the additional RT effect always suppresses the perturbation growth, the mode-coupling might result in the additional RT effect promoting the instability of the constituent Fourier mode. By considering the geometry convergence, the mode-coupling effect and other physical mechanisms, second-order nonlinear solutions are established to predict the RM instability and the additional RT effect in the cylindrical geometry, reasonably quantifying the amplitude growths of each mode, harmonic and coupling. The nonlinear solutions are further validated by simulations considering various initial spectra. Last, the temporal evolutions of the mixed mass and normalized mixed mass of a shocked multimode interface are calculated numerically to quantify the mixing of two fluids in the cylindrical geometry.

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.

‘Freeze-out’ of amplitude growth, i.e. the amplitude growth stagnation of a shocked helium–air interface, is realized through a reflected shock, which produces baroclinic vorticity of the opposite sign to that deposited by the first shock. Theoretically, a model is constructed to calculate the relations among the initial parameters for achieving freeze-out. In particular, if the amplitude growth is within the linear regime at the arrival of the reflected shock, the time interval between the impacts of two shock waves is linearly related to the initial perturbation wavelength, and is independent of the initial perturbation amplitude. Experimentally, an air–SF$_6$ (or air–argon) plane interface is adopted to produce a weak reflected shock. Seven experimental runs with specific initial conditions are examined. For all cases, freeze-out is achieved after the reflected shock impact under the designed conditions.

Shock-induced instability developments of two successive interfaces have attracted much attention, but remain a difficult problem to solve. The feedthrough and reverberating waves between two successive interfaces significantly influence the hydrodynamic instabilities of the two interfaces. The evolutions of two successive slow/fast interfaces driven by a weak shock wave are examined experimentally and numerically. First, a general one-dimensional theory is established to describe the movements of the two interfaces by studying the rarefaction waves reflected between the two interfaces. Second, an analytical, linear model is established by considering the arbitrary wavenumber and phase combinations and compressibility to quantify the feedthrough effect on the Richtmyer–Meshkov instability (RMI) of two successive slow/fast interfaces. The feedthrough significantly influences the RMI of the two interfaces, and even leads to abnormal RMI (i.e. phase reversal of a shocked slow/fast interface is inhibited) which is the first observational evidence of the abnormal RMI provided by the present study. Moreover, the stretching effect and short-time Rayleigh–Taylor instability or Rayleigh–Taylor stabilisation imposed by the rarefaction waves on the two interfaces are quantified considering the two interfaces’ phase reversal. The conditions and outcomes of the freeze-out and abnormal RMI caused by the feedthrough are summarised based on the theoretical model and numerical simulation. A specific requirement for the simultaneously freeze-out of the instability of the two interfaces is proposed, which can potentially be used in the applications to suppress the hydrodynamic instabilities.

Richtmyer–Meshkov instability induced by two successive shock waves is experimentally studied in a specific shock tube. To create two successive shock waves synchronously, a driver section is added between the driver and driven sections of the standard shock tube, and an electronically controlled membrane rupture equipment is adopted. The shock-tube flow after the membranes rupture is well described by combining the shock relations, isentropic wave relations with compatibility relations across the contact surface (region). The new shock tube is capable of generating two successive shock waves with controllable strengths and time interval, and provides a relatively ‘clean’ wave system. Then the developments of single-mode light–heavy interfaces with different initial conditions induced by two successive shock waves are investigated. The initial amplitudes are all small enough such that the first-shocked interface is within the linear growth regime at the arrival of the second shock. The results show that if the pre-second-shock perturbation amplitude is small, the linear, nonlinear and modal evolutions of the double-shocked interface can be reasonably predicted by the existing models proposed for predicting the perturbation growth induced by a single shock. For the double-shocked interface, the second shock provides an additional perturbation velocity field to the original one introduced by the first shock impact. The validity of the linear superposition model indicates that the linear superposition of these two perturbation velocity fields is satisfied. Therefore, a double-shocked interface evolves similarly to a single-shocked interface provided that their postshock amplitudes and linear growth rates are the same.

Shock-tube experiments on various two-bubble and two-spike interfaces are performed to examine the dependence of bubble competition and spike competition on the initial spectra and density ratio of the interface. The differences in the influences of bubble competition and spike competition on the Richtmyer–Meshkov instability are highlighted for the first time. The bubble-competition effect is mainly dependent on the initial spectra of the two-bubble configuration. In contrast, the spike-competition effect is determined by both the initial spectra and density ratio. The extended buoyancy–drag model is adopted to explain the variation of the drag force imposed on the long-wavelength and short-wavelength structures as the initial conditions change. Based on the spectrum analysis, it is found that the constituent modes of two-bubble and two-spike interfaces have different contributions to the long-wavelength and short-wavelength perturbation growths. A generalised, nonlinear, analytical model is then established to quantify the bubble-competition effect and spike-competition effect considering arbitrary initial spectra and density ratio. The bubble-competition effect is believed to be stronger than the spike-competition effect at a high density ratio because it suppresses the high-frequency perturbation growth more evidently.

The two-dimensional (2-D) unsteady shock reflection over a single wedge is studied theoretically and numerically, and the emphasis is placed on the trajectory of the triple point (TP). Skews’ relation and the three-shock theory are, respectively, used for determining the trajectory angles of the corner-generated disturbance and the TP, and, subsequently, a model capable of predicting the TP trajectory is established for 2-D unsteady shock reflections over a single wedge. Then, a systematically numerical study is carried out on the 2-D unsteady shock reflection over a single wedge, including five types of shock reflection with the wedge angle increased and five types of shock reflection with the wedge angle decreased. It is found that the Mach stem is always slightly concavely (convexly) curved for reflections with the wedge angle increased (decreased), which should be caused by corner-generated compression (rarefaction) waves propagating along the Mach stem. The new model reasonably predicts the TP trajectory in all the 2-D unsteady shock reflections, and its performance is related not only to the variation trend of the wedge angle (increase or decrease), but also to the type of shock and the initial wedge angle. Specifically, for the shock reflection with the wedge angle increased (decreased), the model generally provides a slightly better (worse) prediction if the TP trajectory angle calculated by the three-shock theory is compulsively modified. The shock-shock/expansion polar analysis presented can partially explain the model performance for predicting the TP trajectory.

The Richtmyer–Meshkov instability of heavy/light single-mode (SM), trapezoid (TR) and sawtooth (ST) interfaces is studied experimentally by considering the reshock. The TR and ST interfaces can be expanded into Fourier series with a dominant fundamental mode and more high-order modes, recognized as quasi-single-mode ones. In experiments, the distorted interfaces at the time of first reshock arrival develop in the weakly nonlinear stage, ensuring an approximate single-scale function of evolving interface. The results show an evident memory of initial interface shapes: the bubbles and spikes of ST interface after reshock mainly develop in the streamwise direction with sharp heads, while the counterparts of TR interface tend to grow in the spanwise direction. The influences of high-order modes are amplified by the reshock, resulting in significant interface shape dependence of mixing width growths. The amplitude superposition of major odd-order modes promotes the growth rates of mixing widths for the SM and ST cases, different from the TR one. The ST interface has larger mixing width growth rates in comparison with the SM interface, since high-order modes play a great role in promoting the increase of ST amplitudes, while the TR interface has a relatively small one. The linear and nonlinear mixing width growths of SM, TR and ST interfaces before and after reshock are further analysed theoretically, indicating that the fundamental mode still has a predominant influence on the interface evolution after reshock, and the growth behaviours exhibit strong similarities to those for the singly shocked cases.

The shock-induced evolution of a gas layer with two fast/slow interfaces is investigated theoretically and experimentally. Specifically, the gas layer is located between a lighter gas and a heavier gas, forming a light/medium/heavy (LMH) configuration. Linear stability analysis is utilised to derive a new analytical model to quantify the Richtmyer–Meshkov instability (RMI) on the two interfaces of such an A/B/C-type fluid layer. Three quasi-one-dimensional (1-D) LMH fluid layers with different initial layer thicknesses are generated to study the wave patterns and interface motions. A general 1-D theory is established to describe the motions of the shock/rarefaction waves reverberating inside the fluid layer and the displacements of the two interfaces. Six quasi-2-D LMH fluid layers with diverse initial layer-thickness and amplitude combinations are created to explore the hydrodynamic instabilities of the two interfaces. It is found that the interface coupling significantly influences the interface evolution, even resulting in an abnormal phase reversal of a shocked fast/slow interface if the two interfaces are anti-phase and the initial layer is very thin. The specific conditions for the abnormal phase reversal and the instability freeze out are deduced. Moreover, the additional RMI (or Rayleigh–Taylor stabilisation) imposed by the shock (or rarefaction waves) reverberating inside an LMH fluid layer on the first (or second) interface is quantified. It is proved that the reverberating waves inside an LMH fluid layer stabilise the two interfaces. Finally, a nonlinear model is obtained by incorporating the nonlinearity effect into the linear model, which well describes the perturbation growths of the two interfaces in a later regime.

Shock-induced light-fluid-layer evolution is firstly investigated experimentally and theoretically. Specifically, three quasi-one-dimensional helium gas layers with different layer thicknesses are generated to study the wave patterns and interface motions. Six quasi-two-dimensional helium gas layers with diverse layer thicknesses and amplitude combinations are created to explore the Richtmyer–Meshkov instability of a light-fluid layer. Due to the multiple reflected shocks reverberating inside a light-fluid layer, the speeds of the two interfaces gradually converge, and the layer thickness saturates eventually. A general one-dimensional theory is adopted to describe the two interfaces’ motions and the layer thickness variations. It is found that, for the first interface, the end time of its phase reversal determines the influence of the reflected shocks on it. However, the reverberated shocks indeed lead to the second interface being more unstable. When the two interfaces are initially in phase, and the initial fluid layer is very thin, the two interfaces’ spike heads collide and stabilise the two interfaces. Linear and nonlinear models are successfully adopted by considering the interface-coupling effect and the reverberated shocks to predict the two interfaces’ perturbation growths in all regimes. The interfacial instability of a light-fluid layer is quantitatively compared with that of a heavy-fluid layer. It is concluded that the kind of waves reverberating inside a fluid layer significantly affects the fluid-layer evolution.

Shock-induced fluid-layer evolution has attracted much attention but remains a challenge mainly because the coupling between layers remains unknown. Linear solutions are first derived to quantify the layer-coupling effect on the shocked dual-layer evolution. Next, the motions of the waves and interfaces of a dual layer are examined based on the one-dimensional gas dynamics theory. Shock-tube experiments on the dual-layer, single-layer and single-mode interface are then performed to validate the linear solutions and investigate the reverberating waves inside the layers. It is proved that the layer-coupling effect destabilises the dual layer, especially when the initial layers are thin, and the reverberating waves impose additional instabilities on all interfaces. Our findings suggest that a slow/fast configuration with a large thickness in a dual layer can facilitate the suppression of hydrodynamic instabilities.

Shock-tube experiments on eight kinds of two-dimensional multi-mode air–SF$_6$ interface with controllable initial conditions are performed to examine the dependence of perturbation growth on initial spectra. We deduce and demonstrate experimentally that the amplitude development of each mode is influenced by the mode-competition effect from quasi-linear stages. It is confirmed that the mode-competition effect is closely related to initial spectra, including the wavenumber, the phase and the initial amplitude of constituent modes. By considering both the mode-competition effect and the high-order harmonics effect, a nonlinear model is established based on initial spectra to predict the amplitude growth of each individual mode. The nonlinear model is validated by the present experiments and data in the literature by considering diverse initial spectra, shock intensities and density ratios. Moreover, the nonlinear model is successfully extended based on the superposition principle to predict the growths of the total perturbation width and the bubble/spike width from quasi-linear to nonlinear stages.

Scattering kernel models for gas–solid interaction are crucial for rarefied gas flows and microscale flows. However, most existing models depend on certain accommodation coefficients (ACs). We propose here to construct a data-based model using molecular dynamics (MD) simulation and machine learning. The gas–solid interaction is first modelled by 100 000 MD simulations of a single gas molecule reflecting on the wall surface, which is fulfilled by GPU parallel technology. The results showed a correlation of the reflection velocity with the incidence velocity in the same direction, and also revealed correlations that may exist in different directions, which are neglected by the traditional gas–solid interaction model. Inspired by the sophisticated Cercignani–Lampis–Lord (CLL) model, two improved scattering kernels were constructed to better reproduce the probability density of velocity determined from MD simulation. The first one adopts variable ACs which depend on the incidence velocity and the second one combines three CLL-like kernels. All the parameters in the improved kernels are automatically chosen by the machine learning method. Compared with the numerical experiments of a molecular beam, the reconstructed scattering kernels are basically consistent with the MD results.

Investigation on the shock-induced finite-thickness fluid-layer evolution is very desirable but remains a challenge because it not only involves both the Richtmyer–Meshkov instability (RMI) and the Rayleigh–Taylor instability (RTI), but also strongly depends on the waves reverberated inside the layer. We experimentally and theoretically examined the evolution of a shocked $\textrm {SF}_6$ gas layer with a finite thickness surrounded by air. Specifically, three kinds of quasi-one-dimensional $\textrm {SF}_6$ gas layers with different layer thicknesses are generated to study the wave patterns and interface motions, and six types of quasi-two-dimensional $\textrm {SF}_6$ gas layers with diverse layer thicknesses and amplitude combinations are created to explore the interfacial instabilities of the layer. When the initial fluid layer is thin, the two interfaces of the layer coalesce at a late time. The present study is the first to report that except for the RMI induced by a shock wave on the two interfaces, the rarefaction waves (RW) inside the fluid layer induce the additional RTI and decompression effect on the first interface, and the compression waves (CW) inside the fluid layer cause the additional Rayleigh–Taylor stabilisation (RTS) and compression effect on the second interface. A general one-dimensional theory is established to describe the motions of the two interfaces. Linear and nonlinear models are successfully established by considering the interface-coupling effect on the RMI and the additional interfacial instabilities induced by these waves inside the heavy fluid layer. The established models predict well the perturbation growths on the two interfaces at all regimes.

We report the first shock-tube experiments on dual-mode Richtmyer–Meshkov instability (RMI). An extended soap-film technique is adopted to generate a dual-mode gaseous interface such that its initial wavenumber ($k_0$) and phase of the fundamental waves are well controlled. By extracting interfacial contours from the distinct schlieren images, a Fourier analysis is performed from linear to weakly nonlinear stages and the growth of each basic wave is obtained. A noticeable difference between the growth of each basic mode and the corresponding single-mode RMI is observed, which suggests evident mode coupling effects in the dual-mode RMI. For dual-mode interfaces with in-phase $k_0$ and $k_0/2$ waves, the mode coupling suppresses (promotes) the growth of the $k_0$ ($k_0/2$) mode, while for interfaces with anti-phase $k_0$ and $k_0/2$ modes, the growth of the $k_0$ ($k_0/2$) mode is weakly influenced (evidently inhibited). However, for the combination of $k_0$ and $k_0/3$ waves, the mode coupling has a negligible influence on the growth of each basic wave. The modal theory of Haan (Phys. Fluids B, vol. 3, 1991, pp. 2349–2355), originally for multi-mode Rayleigh–Taylor instability, is reformulated for the dual-mode RMI, and it is found that this model overestimates the present experimental results for ignoring the nonlinear saturation. This model is then modified by accounting for both the mode coupling and nonlinear saturation, which well predicts the experimental results not only for the growth of the basic waves but also for the growth of second harmonics.

The convergent Richtmyer–Meshkov instability (RMI) of an $\textrm {SF}_6$ 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.

We report the first experiments on divergent shock-driven Richtmyer–Meshkov instability (RMI) at well-controlled single-mode interfaces. These experiments are performed in a novel divergent shock tube designed by shock dynamics theory. Generally, the perturbation growth can be divided into three successive stages: linear growth, quick reduction in growth rate and instability freeze-out. It is observed that the growth rate at each stage is far lower than its counterpart in planar or convergent geometry due to geometric divergence. We also found that nonlinearity is much weaker than that in planar or convergent RMI, and has a negligible influence on the overall amplitude growth even at late stages when it has become strong. This weak nonlinear effect is because the growth of the third harmonic counteracts its feedback to the fundamental mode. As a consequence, the linear theory of Bell (report no. LA-1321) accounting for geometric divergence and Rayleigh–Taylor (RT) stabilization caused by flow deceleration can reasonably predict the present results from early to late stages. The instability freeze-out at late times is ascribed to the negative growth induced by geometric divergence and RT stabilization, and is also well reproduced by the linear theory.