Richtmyer–Meshkov instability (RMI) at a light–heavy single-mode interface over a wide range of post-shock Atwood numbers $A_1$ is studied systematically through elaborate experiments. The interface generation and $A_1$ variation are achieved by the soap-film technology and gas-layer scheme, respectively. Qualitatively, the nonlinear interface evolution features, including spike, bubble and roll-up structures, are more significant in RMI with higher $A_1$. Quantitatively, both the impulsive model and an analytical linear model perform well in predicting the linear growth rate under a wide range of $A_1$ conditions. For the weakly nonlinear stage, the significant spike acceleration occurring when $A_1$ is high, which is observed experimentally for the first time, results in the evolution law of RMI with high $A_1$ being different from the counterpart with low or intermediate $A_1$. None of the considered nonlinear models is found to be applicable for RMI under all $A_1$ conditions, and the predictive capabilities of these models are analysed and summarized. Based on the present experimental results, an empirical nonlinear model is proposed for RMI over a wide range of $A_1$. Further, modal analysis shows that in RMI with high (low or intermediate) $A_1$, high-order harmonics evolve rapidly (slowly) and cannot (can) be ignored. Accordingly, for RMI with high (low or intermediate) $A_1$, the modal model proposed by Zhang & Sohn (Phys. Fluids, vol. 9, 1997, pp. 1106–1124) is less (more) accurate than the one proposed by Vandenboomgaerde et al. (Phys. Fluids, vol. 14, 2002, pp. 1111–1122), since the former ignores perturbation solutions higher than fourth order (the latter retains only terms with the highest power in time).

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.

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.

‘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.

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.

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.

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.

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.

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.

The interaction of rarefaction waves and a heavy/light interface is investigated using numerical simulations by solving the compressible Euler equations. An upwind space–time conservation element and solution element (CE/SE) scheme with second-order accuracy in both space and time is adopted. Rarefaction waves are generated by simulating the shock-tube problem. In this work, the SF6/air interface evolution under different conditions is considered. First, the gas physical parameters before and after the rarefaction waves impact the interface are calculated using one-dimensional gas dynamics theory. Then, the interaction between the rarefaction waves and a single-mode perturbation interface is investigated, and both the interface evolution and the wave patterns are obtained. Afterwards, the amplitude growth of the interface over time is compared between cases, considering the effects of the interaction period and the strength of the rarefaction waves. During the interaction of the rarefaction waves with the interface, the Rayleigh–Taylor instability induced by the rarefaction waves is well predicted by modifying the nonlinear model proposed by Zhang & Guo (J. Fluid Mech., vol. 786, 2016, pp. 47–61), considering the variable acceleration. After the rarefaction waves leave the interface, the equivalent Richtmyer–Meshkov instability is well depicted by the nonlinear model proposed by Zhang et al. (Phys. Rev. Lett., vol. 121(17), 2018, 174502), considering the growth rate transition from Rayleigh–Taylor instability to Richtmyer–Meshkov instability. The differences in the heavy/light interface amplitude growth under the rarefaction wave condition and the shock wave condition are compared. The interface perturbation is shown to be more unstable under rarefaction waves than under a shock wave.

The regular reflection to Mach reflection ($\text{RR}\rightarrow \text{MR}$) transition in inviscid perfect air for shock reflection over convex and straight wedges is investigated. Provided that the variation of shock intensity only has a second-order effect on the wave transition, the possible cases for the occurrence of the $\text{RR}\rightarrow \text{MR}$ transition for curved shock reflection over a wedge are discussed. For a planar shock reflecting over a convex wedge, four different flow regions are classified and the mechanism of the disturbance propagation is interpreted. It is found that the flow-induced rarefaction waves exist between disturbances generated from neighbouring positions and isolate them. For a curved shock reflecting over a convex wedge, although the distributions of the flow regions are different from those in planar shock reflection, the analysis for the planar shock case can be extended to curved shock cases as long as the wedge is convex. When a diverging shock reflects off a straight wedge, the flow-induced rarefaction waves are absent. However, the disturbances generated earlier cannot overtake the reflection point before the pseudo-steady criterion is satisfied. In the cases considered, the flow in the vicinity of the reflection point will not be influenced by the unsteady flow caused by the shock intensity and the wedge angle variations. This is clearly a local property of the shock–wall interaction, no matter what the history of the shock trajectory is. For validation, extensive inviscid numerical simulations are performed, and the numerical results show the reliability of the pseudo-steady criterion for predicting the $\text{RR}\rightarrow \text{MR}$ transition on a convex wedge.

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.

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.

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 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.

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.

Experimental and numerical investigations on the interaction of a planar shock wave with two-dimensional (2-D) and three-dimensional (3-D) light gas cylinders are performed. The effects of initial interface curvature on flow morphology, wave pattern, vorticity distribution and interface movement are emphasized. In experiments, a wire-restriction method based on the soap film technique is employed to generate N$_{2}$ cylinders surrounded by SF$_{6}$ with well-characterized shapes, including a convex cylinder, a concave cylinder with a minimum-surface feature and a 2-D cylinder. The high-speed schlieren pictures demonstrate that fewer disturbance waves exist in the flow field and the evolving interfaces develop in a more symmetrical way relative to previous studies. By combining the high-order weighted essentially non-oscillatory construction with the double-flux scheme, numerical simulation is conducted to explore the detailed 3-D flow structures. It is indicated that the shape and the size of 3-D gas cylinders in different planes along the vertical direction change gradually due to the existence of both horizontal and vertical velocities of the flow. At very early stages, pressure oscillations in the vicinity of evolving interfaces induced by complex waves contribute much to the deformation of the 3-D gas cylinders. As time proceeds, the development of the shocked volume would be dominated by the baroclinic vorticity deposited on the interface. In comparison with the 2-D case, the oppositely (or identically) signed principal curvatures of the concave (or convex) SF$_{6}$/N$_{2}$ boundary cause complex high pressure zones and additional vorticity deposition, and the upstream interface from the symmetric slice of the concave (or convex) N$_{2}$ cylinder moves with an inhibition (or a promotion). Finally, a generalized 3-D theoretical model is proposed for predicting the upstream interface movements of different gas cylinders and the present experimental and numerical findings are well predicted.

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.

A sediment core from Hulun Lake, Inner Mongolia was analyzed for species assemblages and shell chemistry of ostracodes to investigate changes in the hydrology and climate of the East Asian summer monsoon margin during the Holocene. Darwinula stevensoni was abundant, Ilyocypris spp. scarce, littoral ostracodes absent and Mg/Ca, Sr/Ca and δ18O were low 11,100 to 8300 yr ago, indicating high lake levels and cool/fresh waters. Darwinula stevensoni declined largely, Ilyocypris spp. throve, littoral ostracodes were rare and chemical indicators remained in low values 8300 to 6200 yr ago, suggesting that the lake continued high stands but water became warm. The lake then contracted and water became cool/brackish 6200 to 4300 yr ago. Littoral ostracodes flourished 4300 to 3350 yr ago, marking the lowest lake levels of the entire Holocene. The lake level recovered and water salinity decreased 3350 to 1900 yr ago. From 1900 to 500 yr ago, the lake maintained the preceding status albeit lowered stands and increased salinities 1100 to 800 yr ago. During the recent 500 yr, the lake expanded and water salinity decreased. The data imply that the East Asian summer monsoon did not intensify until 8300 yr ago and weakened dramatically 4300 to 3350 yr ago.