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The experimental apparatus. A PC controls the diagnostic system. The light source to the Schlieren optical system is a Nd:YAG doubled frequency laser.
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The present article describes an experimental study that is a part of an integrated theoretical (Rikanati et al. 2003) and experiential investigation of the Richtmyer Meshkov (RM) hydrodynamic instability that develops on a perturbed contact surface by a shock wave. The Mach number and the high initial-amplitude effects on the evolution of the sing...
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... wavelength is much smaller than the initial amplitude ~ a 0 k Ͻ Ͻ 1 ! and incompressible flow. In recent years, efforts have been made to study the evolution of the Richtmyer–Meshkov instability in the case of high Mach numbers. Shock-tube experiments where conducted by Aleshin’s research group ~ Aleshin et al ., 1990, 1997 ! using moderate Mach numbers ~ 2.5–3.5 ! , various initial conditions, and different test gas combinations ~ He-Xe, Ar-Kr, He-Xe in heavy to light and light to heavy arrange- ments ! . In their work, an effort was made to map the behavior for the instability and to quantify the differences between the various regimes. Three regimes were defined as “soft” where the nonlinear theory is applicable, “hard,” and “irreg- ular,” where the nonlinear behavior was observed immedi- ately at the initial stages ~ shear instabilities and asymmetry between the bubbles and spikes ! . The hard and irregular regions were distinguished from the soft one by the high Atwood number, high initial-amplitude and high-Mach number ~ for more details, see Aleshin et al ., 1997 ! . A reduction in the initial velocity of the perturbation from the linear velocity predicted by the Richtmyer and Meyer-Blewett models in the light to heavy and heavy to light configurations was observed in the hard and irregular regions. Dimonte et al . ~ 1996 ! conducted experiments with higher Mach numbers. The experiments were conducted on the NOVA laser at Lawrence Livermore National Laboratory ~ LLNL ! . The focusing of the laser beams into a radiation enclosure ~ indirect drive configuration ! generated shock waves with Mach numbers of M ; 15 in Be ~ r ϭ 1.7 g 0 cc ! to foam ~ r ϭ 0.12 g 0 cc ! configurations. In these experiments, the initial amplitudes ranged from a 0 k ; 0.2 to a 0 k ; 4, which is well above the applicability limit of the linear models. In some of these experiments with a 0 k . 4, large reductions of the initial instability growth velocities from those predicted by the linear classical model were observed, whereas in others with a 0 k Յ 1, the agreement was good. It is commonly assumed that the reduction was due to high Mach number effects ~ see, e.g., Aleshin et al ., 1997; Holmes et al ., 1999 ! . In our theoretical complementary study ~ see Rikanati et al ., 2003 ! the reduction of the initial instability growth velocity as compared to the predictions of a new nonlinear classical model is presented and two models were introduced and supported by two-dimensional ~ 2D ! simulations. The models, which described correctly the reduction, took into ac- count the effect of the high initial amplitude ~ geometrical effect ! —the “vorticity deposition” model—and the shock- interface proximity effect ~ high Mach number effect ! —the “wall” model. It was found that the geometric effect was dominant only at the initial stage. At the late stage, the effect was diminished and the bubble front floated in its asymptotic velocity. The Mach number effect reduced the initial velocity. In the present study, two sets of shock-tube experiments are reported. One set has large initial amplitudes and low Mach numbers demonstrating the reduction in the initial instability growth velocity as compared to the nonlinear classical model, and gives us to study the late stage evolution with nonlinear initial conditions. The other set has a moderate Mach number of M ϭ 2 and a linear initial amplitude ~ a 0 k , 1 ! demonstrating the high Mach number effect on the instability at the late nonlinear stages of the flow. The experiments were performed in a 5.5-m-long horizontal double-diaphragm shock tube with an 8 cm ϫ 8 cm cross section. A thin membrane separated the two gases ~ in this kind of experiments, the effect of the membrane is negligi- ble; see Erez et al ., 2000 ! . The evolution of the shock-wave- induced mixing zone was measured by recording a series of Schlieren photographs using a Nd:YAG frequency-doubled laser pulsed at intervals of about 20 to 200 m s and a shutter- less rotating-prism camera. The photographs were analyzed using a computerized image analysis. Figure 1 is a sche- matic diagram of the experimental apparatus. To generate a shock wave having a Mach number in the range 1.2–2.0, the driver section was first filled with air or He until it reached the pressure that was required to rupture a 0.14-mm-thick diaphragm consisting of one or two layers of mylar sheet. The strength and velocity of the shock wave were measured with piezoelectric pressure transducers that were flush mounted on the shock-tube walls. The arrival of the shock wave at the first pressure transducer was used to trigger the diagnostic timing sequence. A thin membrane was placed between the two investi- gated gases in the test section. Upon the rupture of this membrane by the shock wave, the mixing process began. Windows were built into the side walls of the test section. Their height spanned the entire 8-cm height of the test section. Their length was 20 cm, beginning at the frame holding the membrane. The gases on both sides of the membrane, in the test section, were at an ambient pressure. The apparatus was controlled by a PC computer system that operated the pneumatic valves and slow rate sensors. The system was equipped with timing and DAQ cards and operated using LabVIEW software. To investigate the high-initial amplitude effect, a set of experiments with varied a Ϫ 0 k was performed. All the experiments were done with an air 0 SF 6 gas combination ~ light to heavy combination, Atwood number A ϭ 0.67 ! and a Mach number of M ϭ 1.2. Table 1 summarizes the initial conditions. The high Mach number study was done using air 0 SF 6 gas combination with M ϭ 2. An experimental verification of the high initial-amplitude dominance in the above experiments was obtained ...
Citations
... Besides the laser-driven experiments, there are a few shock-tube experiments on RMI at a light-heavy interface with M ≥ 2.0. Using a solid membrane with wire support to separate different gases, Sadot et al. (2003) investigated the evolution of an air-SF 6 interface impacted by a shock wave with M = 2. However, the wire support may affect the perturbation evolution. ...
... In this work, the initial single-mode air-SF 6 interface is generated through polyester film, as illustrated in figure 1 (b). Note that the solid membrane employed in previous works (Meshkov 1969;Sadot et al. 2003) is made of nitrocellulose, which is brittle and susceptible to cracking under strain. As a result, grid support, which can significantly influence the flow evolution, was required to form the initial interface. ...
... For the overall interface, the ZS, SEA and DR models overestimate its amplitude growth, whereas the MIK and ZG models offer reasonable predictions. For the bubble, its early-time growth is slower than the model predictions due to the shock proximity effect (Sadot et al. 2003): the transmitted shock remains close to the shocked interface for a relatively long duration, inhibiting the evolution of the bubbles and flattening them. Subsequently, under the effect of the pressure perturbations introduced by transverse shocks, i.e. the secondary compression effect, the bubble growth saturates. ...
We report the first shock-tube experiments on Richtmyer-Meshkov instability at a single-mode light-heavy interface accelerated by a strong shock wave with Mach number higher than 3.0. Under the proximity effect of the transmitted shock and its induced secondary compression effect, the interface profile is markedly different from that in weakly compressible flows. For the first time, the validity of the compressible linear theory and the failure of the impulsive model in predicting the linear amplitude evolution in highly compressible flows are verified through experiments. Existing nonlinear and modal models fail to accurately describe the perturbation evolution, as they do not account for the shock proximity and secondary compression effects on interface evolution. The shock proximity effect manifests mainly in the early stages when the transmitted shock remains close to the interface, while the effect of secondary compression manifests primarily at the period when interactions of transverse shocks occur at the bubble tips. Based on these findings, we propose an empirical model capable of predicting the bubble evolution in highly compressible flows.
... However, for a moderate or strong shock, the transmitted shock (TS) is close to the interface for a long time and the transverse waves behind the shock continuously affect the interface evolution (called shock proximity effect), giving rise to an evident compressibility effect at late stages. This has been confirmed by several independent shock-tube experiments (Sadot et al. 2003;Puranik et al. 2004;Motl et al. 2009), in which the bubbles were observed to be flattened by the transverse waves at the late stage. The coexistence of compressibility and nonlinearity at late stages poses a great challenge for theoretical treatment. ...
... As time proceeds, the TS propagates forwards with a gradually decaying amplitude and finally recovers to a uniform cylindrical shock (491 μs). It is worth noting that no evident spike and bubble structures are observed even at the late stage when intensifying the incident shock, which differs from the planar RM instability (Sadot et al. 2003;Motl et al. 2009). This phenomenon exists uniquely in divergent RM instability. ...
Richtmyer–Meshkov (RM) instability at a single-mode interface impacted by a cylindrical divergent shock with low to moderate Mach numbers is investigated experimentally. The motion of an unperturbed interface is first examined to obtain the background flow. The shocked interface moves uniformly at the early stage, but later decelerates. The stronger the incident shock, the larger the interface deceleration, which is reasonably predicted by a one-dimensional model considering the effect of postshock non-uniformity. Such a deceleration greatly inhibits the growths of harmonics of an initially perturbed interface and, consequently, the divergent RM instability presents very weak nonlinearity from early to late stages. Particularly, higher-Mach-number cases present weaker nonlinearity due to larger deceleration there. This abnormal linear growth regime is reported for the first time. Benefiting from this, the incompressible linear model holds validity at all stages of divergent RM instability. It is also found that compressibility inhibits the initial growth rate, but produces a weak influence on the subsequent instability growth.
... As a result, in relatively high Mach number cases, the transmitted shock recedes slowly from the interface (Glendinning et al. 2003;Motl et al. 2009). This results in changes in pressure behind the transmitted shock influencing the interface perturbation growth for a relatively long time; thus, compressibility effects become significant in higher Mach number cases (Sadot et al. 2003;Guo et al. 2020;Zhang et al. 2022). The presence of compressibility effects adds complexity to the coupling between the two interfaces, possibly influencing the realization of freeze-out. ...
The shock wave accelerating a heavy fluid layer can induce reverberating waves that continuously interact with the first and second interfaces. In order to manipulate the perturbation growths at fluid-layer interfaces, we present a theoretical framework to eliminate the reverberating waves. A model is established to predict the individual freeze-out (i.e. stagnation of perturbation growth) for the first and second interfaces under specific flow conditions determined based on the shock dynamics theory. The theoretical model quantifies the controllable parameters required for freeze-out, including the initial amplitudes of the first and second interfaces, the interface coupling strength and the maximum initial layer thickness preventing the second interface's phase reversal. The effectiveness of the model in predicting individual freeze-out for the first and second interfaces is validated numerically over a wide range of initial conditions. The upper and lower limits of initial amplitudes for the freeze-out of the whole fluid-layer width growth are further predicted. Within this amplitude range, a slightly higher initial amplitude for the second interface is specified, effectively arresting the growth of the entire fluid-layer width before the phase reversal of the second interface.
... 11 To theoretically predict the linear growth rate of the RM instability, by modeling the shock impact as an impulsive acceleration, Richtmyer first proposed the impulsive model under incompressible conditions. 1 The impulsive model can reasonably predict the linear growth rate of a light/heavy interface when the incident shock is not strong [12][13][14] but will overestimate the linear growth rate under strong shock conditions. [15][16][17] It was found that the high Mach number effect can dramatically change the flow behaviors. 8,15 A reduction of linear growth rate was observed in experiments performed by Motl et al. 17 They ascribed the bubble-growth suppression to the shock proximity effect, which is specifically significant under strong shock conditions. ...
... [15][16][17] It was found that the high Mach number effect can dramatically change the flow behaviors. 8,15 A reduction of linear growth rate was observed in experiments performed by Motl et al. 17 They ascribed the bubble-growth suppression to the shock proximity effect, which is specifically significant under strong shock conditions. ...
Experimental and numerical studies on the evolution of shock-accelerated SF6/air interface with small initial amplitude are conducted. The effect of compressibility on the early development of perturbation is highlighted by varying shock intensity and fluid properties. The startup process is analyzed when rarefaction waves are reflected and the characteristic time of the startup process is provided. The relationship between the phase inversion process and the startup process under different incident shock strengths is clarified. According to the startup time, a new start point for normalization is given, which can better normalize the amplitude growth at the early stage. In addition, the effects of incident shock strength and physical properties of fluids on the linear growth rate are highlighted through numerical simulations. The incompressible linear model loses validity when the incident shock is strong, and the existing rotational model is verified to provide excellent predictions under any shock strengths. The decrease in adiabatic exponent of the heavy fluid or the increase in adiabatic exponent of the light fluid can reduce the linear growth rate. As the absolute value of Atwood number increases, the adiabatic exponent of the heavy fluid has a more significant effect on the linear growth than that of the light fluid.
... In other words, although Sadot's intention was to create a single-mode interface, the resulting interface resembles a V-shape. Given that V-shaped interfaces share an 81 % similarity with purely single-mode cases (Mikaelian 2005), Sadot et al. (1998) habitually referred to a V-shaped case as a single-mode case, as described in their later study (Sadot et al. 2003). This habitual designation is not unique and is evident in other literature (Farley et al. 1999;Mohaghar et al. 2017Mohaghar et al. , 2019. ...
We report the first experiments on hydrodynamic instabilities of a single-mode light/heavy interface driven by co-directional rarefaction and shock waves. The experiments are conducted in a specially designed rarefaction-shock tube that enables the decoupling of interfacial instabilities caused by these co-directional waves. After the impacts of rarefaction and shock waves, the interface evolution transitions into Richtmyer–Meshkov unstable states from Rayleigh–Taylor (RT) stable states, which is different from the finding in the previous case with counter-directional rarefaction and shock waves. A scaling method is proposed, which effectively collapses the RT stable perturbation growths. An analytical theory for predicting the time-dependent acceleration and density induced by rarefaction waves is established. Based on the analytical theory, the model proposed by Mikaelian ( Phys. Fluids , vol. 21, 2009, p. 024103) is revised to provide a good description of the dimensionless RT stable behaviour. Before the shock arrival, the unequal interface velocities, caused by rarefaction-induced uneven vorticity, result in a V-shape-like interface. The linear growth rate of the amplitude is insensitive to the pre-shock interface shape, and can be well predicted by the linear superposition of growth rates induced by rarefaction and shock waves. The nonlinear growth rate is higher than that of a pure single-mode case, which can be predicted by the nonlinear models (Sadot et al. , Phys. Rev. Lett. , vol. 80, 1998, pp. 1654–1657; Dimonte & Ramaprabhu, Phys. Fluids , vol. 22, 2010, p. 014104).
... When a shock wave accelerates a single-mode interface with a high initial amplitude (generally a 0 =k > 0:1 with a 0 and k being the initial amplitude and wavelength), the impulsive model was also found to overestimate the linear growth rate. [21][22][23] As the primary incident shock (IS) passes through the interface with high initial amplitudes, many additional reverberating waves are generated. These waves propagate along the interface, introducing the secondary compression effect that causes the reduction of the amplitude growth rate. ...
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 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 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 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.
... Four sinusoidal interfaces with different initial amplitudes (a 0 ) and wavelengths (λ) are realized in the shock-tube experiments. The detailed parameters correspond- 42 2 Shock-Driven Multi-mode Interface Evolution ing to the initial conditions for each case (denoted by λ − a 0 ) are listed in Table 2.2. ...
... The cavity has been observed in previous numerical simulations [37][38][39] on saw-tooth interfaces. Still, it has never been found in previous experiments, probably due to the boundary layer near the shock-tube walls [39][40][41] or the wire mesh used to form the interface [42,43]. Our work provides the first experimental evidence for the existence of the cavity of a shocked saw-tooth interface. ...
Richtmyer-Meshkov (RM) instability occurs when an initially perturbed interface separating different materials is driven by an impulsive acceleration (e.g., shock wave). Later, the perturbation on the interface grows, and, eventually, the mixing layer might transit to turbulence. RM instability plays an essential role in many applications, such as inertial confinement fusion (ICF), supernova explosion, and scramjet engine. It has been widely used to study gas dynamics, vortex dynamics, and turbulence. Therefore, RM instability has attracted lots of attention worldwide, such as the Lawrence Livermore National Laboratory and the Los Alamos National Laboratory in the U.S.A., the Commissariat a l’Energie Atomique Laboratory in France, and the China Academy of Engineering Physics. The RM instability of a single-mode perturbation interface attracted the most attention because of its simplest mathematic pattern. However, the initial interface perturbation in applications is always random, i.e., multi-mode. Nevertheless, the dependence of the multi-mode RM instability on the initial perturbation spectrum has not been fully understood yet. Moreover, an ICF target consists of multiple layers of different materials in spherical geometry. However, there was limited research on the feedthrough between the interfaces and the reverberating waves involved in a shocked multi-layer system. In addition, an ICF target consists of different phases, including solid, liquid, gas, plasma, etc. Still, the influence of the phase-transition on a shocked multi-phase configuration has been scarcely explored. The present study experimentally and theoretically investigates the RM instability separately coupled with the multi-mode perturbation, the multi-layer system, and the multi-phase configuration.
First, we developed a soap film technique to generate shape-controllable two-dimensional (2D) single-mode interfaces, quasi-single-mode interfaces, multi-mode interfaces, and three-dimensional (3D) interfaces with a minimum-surface feature. Experiments were performed in a horizontal shock-tube with a large-aspect-ratio cross-section. The interfacial morphologies of a shocked single-mode interface captured from the experiments show that the instability evolution involves the slightest experimental uncertainty among all existing results. The performances of the linear model and nonlinear models were thoroughly examined through the temporal variations of the interface amplitude growths. Next, four types of quasi-single-mode interfaces dominated by the fundamental mode were generated with the improved soap film technique. It was found that the mode-competition can be ignored at the early nonlinear regime of the RM instability of a quasi-single-mode interface. A simple nonlinear theory was established to describe the mixing width growths by summing the magnitude growths of a finite number of constituted modes ignoring the mode-competition. More constituted modes needed in the simple nonlinear theory to match the experiments indicate the more pronounced deviation of the quasi-single-mode perturbation from the single-mode one. Later, the RM instability of various multi-mode interfaces consisting of multiple dominated modes was explored. A universal nonlinear model for the magnitude growth of each constituted mode and the mixing width growth of the multi-mode interface was established considering the mode-competition and nonlinearity. The universal nonlinear model was validated with our elaborate shock-tube experiments and the data extracted from the literature considering various initial conditions. Last, the RM instability of a 3D interface with a minimum-surface feature was figured out. The universal nonlinear model was extended to describe the 3D RM instability considering the initial 3D interface spectrum and the coupling between 3D modes.
Second, the hydrodynamic instabilities of a shocked 2D finite-thickness gas layer were experimentally and theoretically examined. Using the extended soap film technique, we generated shape-controllable and thickness-controllable discontinuous heavy gas layers and light gas layers such that the instability of each interface of a layer was concerned. The interface-coupling and the reverberating waves inside a gas layer were found to have a significant influence on the hydrodynamic instabilities. It was the first to quantify the additional Rayleigh-Taylor (RT) instability imposed by rarefaction waves and the additional RT stabilization induced by compression waves on a shocked heavy gas layer. Moreover, the additional RM instability caused by the reverberating shocks inside a light gas layer was well described. In addition, the shock-driven dual layer evolution was theoretically and experimentally investigated for the first time. The coupling between the two layers plays a significant role in influencing the RM instability of the three interfaces of a dual layer. The reverberating waves inside a multi-layer system have non-negligible and diverse influences on the three interfaces. It is evident that the shock-driven hydrodynamic instabilities of a semi-infinite interface, a single layer, and a dual layer are categorically different.
Third, the interaction of a shock wave and a 3D water droplet embedded with a vapour bubble was experimentally studied for the first time. The vapour bubble inside a droplet was generated by depressurizing the ambient gas pressure to the saturation pressure of water in the driven section of a shock-tube. It was proved that the relative size and position of the vapour bubble to the droplet influence the hydrodynamic instabilities. The phase-transition accelerates the breakup of the droplet. The transverse jet inside the droplet induced by RM instability and other mechanisms was clearly observed. A modified Rayleigh-Plesset equation is derived to predict the bubble collapse within a droplet, validated with our shock-tube experiments.
... However, Glendinning et al. 28 pointed out that for a heavy-light configuration where the transmitted shock wave moves much faster than the shocked interface, the shock proximity effects can still be less significant even for very high Mach numbers, unless a high initial amplitude is imposed on the interface. Rikanati et al. 27 and Sadot et al. 22 performed two sets of shock-tube experiments: high initial amplitudes with a low-Mach incident shock and small initial amplitudes with a moderate-Mach incident shock, to highlight the high amplitude effect and the high Mach number effect. Their results suggested that the high amplitude effect is the dominant one rather than the high Mach number effect, as suggested by others. ...
... The shock proximity effects are significant under high initial amplitude and high Mach number conditions. According to the data in Table II, the initial amplitude effect changes the growth rate more obviously relative to the shock proximity effects within the scope of the initial conditions in the present work, which coincides with the conclusions achieved by others 22,27 where the high amplitude effect is a dominant one rather than the high Mach number effect. ...
Deep neural networks for nonlinear model order reduction of unsteady flows Physics of Fluids 32, 105104 (2020); https://doi.org/10.1063/5.0020526 Experimental investigation of the transonic shock-wave/boundary-layer interaction over a shock-generation bump Physics of Fluids 32, 106102 (2020); https://doi.org/10.1063/5.0018763 Ultrafast tomographic particle image velocimetry investigation on hypersonic boundary layers Physics of Fluids 32, 094103 (2020); https://doi. ABSTRACT 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/SF 6 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.
... The amplitude growth rate was found to deviate from the prediction by the impulsive model, and this was ascribed to compressible effects. However, Rikanati et al. (2003) and Sadot et al. (2003) believed the effect of the high initial amplitude on the instability evolution was overlooked in the analysis above. Rikanati et al. (2003) proposed a reduction factor to modify the impulsive theory for initial sinusoidal and chevron shaped interfaces with high amplitude. ...
... The model matches experiments with low Mach numbers and also high Mach numbers (Dimonte et al. 1996;Aleshin et al. 1997). As a result, Rikanati et al. (2003) and Sadot et al. (2003) concluded that the high-amplitude effect is the dominant reason for the deviation of the experimental growth rate from the impulsive theory, even at high Mach numbers. For the multi-mode interface, Bakhrakh et al. (1995) experimentally investigated the differences between conjugated circle arcs, 'step-like' and 'saw-tooth' interfaces. ...
... A cavity is formed on the spike centre (1079 µs), and for the same reason as that in the single-mode case. Similarly, the cavity has been also observed in many numerical simulations (Hawley & Zabusky 1989;McFarland, Greenough & Ranjan 2011;Wang et al. 2012), but has never been found in previous experiments, probably due to the boundary layer effect on the initial interface (Wang et al. 2012;McFarland et al. 2014McFarland et al. , 2015 or the wire mesh used to form the interface Sadot et al. 2003). Our work provides the first experimental evidence for the existence of the cavity in the shocked saw-tooth interface. ...
Experiments on Richtmyer–Meshkov instability of quasi-single-mode interfaces are performed. Four quasi-single-mode air/ 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.
... Although the models, such of those of Holmes et al. and Hurricane et al., which reduced the initial growth rate and assumed a monotonically decreasing growth rate thereafter, correctly predicted the average growth, but they did not correctly predict the growth rate as a function of time. Sadot et al. (1998Sadot et al. ( , 2003 and Rikanati et al. (2003) performed Mach 1.2 shock-tube experiments with sawtooth initial perturbations. Numerical simulations with Mach numbers ranging from 1.2 to 15.3 were performed to characterize the experiments of Aleshin et al. (1997) and Dimonte et al. (1996b). ...
... Rikanati et al. (2003) and Glendinning et al. (2003) found that the model of Zhang and Sohn (1997a) as well as the models based on vortex evolution appropriate for accounting for the behavior observed. Sadot et al. (2003) also found good agreement between the shock-tube experiment predictions and the vorticity deposition model at Mach = 1.2. The vorticity deposition model was also helpful for Rikanati et al. (2003) when producing a curve for the reduction factor of the initial velocity. ...
... The vorticity deposition model was also helpful for Rikanati et al. (2003) when producing a curve for the reduction factor of the initial velocity. Fig. 2.20 shows the experimental results of Aleshin et al. (1990), Dimonte et al. (1996b) and Sadot et al. (2003) for moderate and high Mach number experiments. As can be seen from Fig. 2.20, the reduction in all of the experiments fit a single curve. ...
