Bubble Front Research Articles

Non-linearities in cosmological bubble wall dynamics

A precise modelling of the dynamics of bubbles nucleated during first-order phase transitions in the early Universe is pivotal for a quantitative determination of various cosmic relics, including the stochastic background of gravitational waves. The equation of motion of the bubble front is affected by the out-of-equilibrium distributions of particle species in the plasma which, in turn, are described by the corresponding Boltzmann equations. In this work we provide a solution to these equations by thoroughly incorporating the non-linearities arising from the population factors. Moreover, our methodology relies on a spectral decomposition that leverages the rotational properties of the collision integral within the Boltzmann equations. This novel approach allows for an efficient and robust computation of both the bubble speed and profile. We also refine our analysis by including the contributions from the electroweak gauge bosons. We find that their impact is dominated by the infrared modes and proves to be non-negligible, contrary to the naive expectations.

Downhole detection of gas kick using low-frequency elastic wave: Multiphysics modeling and its implications

Gas kick is a common and high-risk drilling trouble in geo-energy engineering, especially for deep-water drilling and ultra-deep well drilling. The most favorable way of early detection of gas kick is to move the detection from the wellhead or near surface to the downhole. In this paper, a new conception of downhole detection of gas kick using low-frequency elastic wave was put forward. The framework of coupling the multiple physic processes of gas-liquid two-phase annulus flow, bubble migration and low-frequency elastic wave propagation during gas kick was developed. The characteristic responses of low frequency elastic wave to gas kick were quantitatively analyzed based on multiphysics modeling under the ideal case and different levels of background gas (BGG), respectively. The modeling results indicated that: (i) The velocity decreases cliff-like and the attenuation coefficient increases significantly at the gas-kick bubble front. The change magnitudes of the velocity and the attenuation coefficient increase with the gas intrusion rate, and decrease with the pump displacement. The change magnitude of attenuation coefficient decreases with mud density, while the increase of velocity is not sensitive to the mud density. (ii) For the ideal case of the vertical well, the effective detection within the depth section of (2014–2568) meter could identify gas kick about (14.3–29.2) minutes earlier than the conventional pit-gain method. The gas kick could be identified earlier when the deviation angle is smaller and/or the monitoring point goes deeper. (iii) The changing magnitudes and rates of the velocity and the attenuation coefficient decrease with the BGG. The downhole detection of gas kick using low-frequency elastic wave should be reliable when the BGG is lower than 5%. The effects of rock cuttings, phase transition of the gas, and drill-string vibrations should be further investigated in future study.

Pipe to annular flow conversion: Numerical study

Large Eddy Simulation (LES) of turbulent flow at the entrance to an annular pipe section has been performed. The flow over a single circular rod, coaxially immersed in a circular pipe is considered. The Reynolds number, based on mean velocity and hydraulic diameter of the annular section, is ReDh=40530. The study aims to gain insights into the turbulence characteristics of the primary and secondary separation bubbles, developing on a side surface of the rod. Key findings include tiny toroidal vortices in the primary bubble's front, forming a vortex train with intermittently shed vortex structures. Large-scale helical stripes have been reproduced at the entrance to the annular section. Tilting of the axially-oriented streaks was observed close to the rod surface. It resulted in a slight anisotropy of the normal Reynolds stresses. The LES data could refine classic Reynolds-averaged Navier-Stokes-based turbulence models.

Experimental observation of a confined bubble moving in shear-thinning fluids

The motion of a long gas bubble in a confined capillary tube is ubiquitous in a wide range of engineering and biological applications. While the understanding of the deposited thin viscous film near the tube wall in Newtonian fluids is well developed, the deposition dynamics in commonly encountered non-Newtonian fluids remains much less studied. Here, we investigate the dynamics of a confined bubble moving in shear-thinning fluids with systematic experiments, varying the zero-shear-rate capillary number $Ca_0$ in the range of $O(10^{-3}\unicode{x2013}10^2)$ considering the zero-shear-rate viscosity. The thickness of the deposited liquid film, the bubble speed and the bubble front/rear menisci are measured, which are further rationalized with the recent theoretical studies based on appropriate rheological models. Compared with Newtonian fluids, the film thickness decreases for both the carboxymethyl cellulose and Carbopol solutions when the shear-thinning effect dominates. We show that the film thickness follows the scaling law from Aussillous & Quéré (Phys. Fluids, vol. 12, no. 10, 2000, pp. 2367–2371) with an effective capillary number $Ca_e$ , considering the characteristic shear rate in the film as proposed by Picchi et al. (J. Fluid Mech., vol. 918, no. A7, 2021, pp. 1–30). $Ca_e$ is calculated by the Carreau number and the power-law index from the Carreau–Yasuda rheological model. The shear-thinning effect also influences the bubble speed and delays the transition to the parabolic region in the bubble front and rear menisci. In particular, a high degree of undulations on the bubble surface results in an intricate rear viscosity distribution for the rear meniscus and the deviation between the experiments and theory may require a further investigation to resolve the axial velocity field. Our study may advance the fundamental understandings and engineering guidelines for coating processes involving thin-film flows and non-Newtonian fluids.

Interactions between a cavitation bubble and solidification front under the effects of ultrasound: Experiments and lattice Boltzmann modeling.

The phenomena of melting and dendritic fragmentation are captured by using an in-situ device during the ultrasound-assisted solidification of a succinonitrile-acetone (SCN-ACE) alloy. The experimental results show that the dendrite arms detach from primary trunk due to the melting of the solid phase, which is caused by a moving ultrasound cavitation bubble. To quantify the interactions between the ultrasound cavitation bubble and the solidification front, a coupled lattice Boltzmann (LB) model is developed for describing the fields of temperature, flow, and solid fraction, and their interactions. The multi-relaxation-time (MRT) scheme is applied in the LB model to calculate the liquid-gas flow field, while the Bhatnagar-Gross-Krook (BGK) equation is executed to simulate the evolution of temperature. The kinetics of solidification and melting are calculated according to the lever rule based on the SCN-ACE phase diagram. After the validation of the LB model by an analytical model, the morphologies of the cavitation bubble and solidification front are simulated. It is revealed that the solidification interface melts due to the increase of the temperature nearby the cavitation bubble in ultrasonic field. The simulated morphologies of the cavitation bubble and solidification front are compared well with the experimental micrograph. Quantitative investigations are carried out for analyzing the melting rate of the solidification front under different conditions. The simulated data obtained from LB modeling and theoretical predictions reasonably accord with the experimental results, demonstrating that the larger the ultrasonic intensity, the faster the melting rate. The present study not only reveals the evolution of the solidification front shape caused by the cavitation bubbles, which is invisible in the ultrasound-assisted solidification process of practical alloys, but also reproduces the complex interactions among the temperature field, acoustic streaming, and multi-phase flows.

A numerical study of flow boiling in a microchannel using the local front reconstruction method

AbstractThe rapid advances in performance and miniaturization of electronic devices require a cooling technology that can remove the produced heat at a high rate with small temperature variations, as is obtained in flow boiling. To obtain insight in flow boiling, we performed numerical simulations in a 200 μm square microchannel using the local front reconstruction method. Besides validation with literature results, a parametric study shows an increasing heat removal rate and bubble growth rate with increasing wall temperature, liquid mass density, and liquid heat capacity and decreasing inlet velocity indicating the importance of phase change compared to convective transport. Finally, the heat transfer in the liquid film is studied using a Nusselt number defined with the film thickness, which is comparable to Nusselt number for falling films on hot surfaces. It is observed that convective effects are more pronounced at the bubble rear compared to the bubble front.

Numerical simulation of single- and multi-mode Rayleigh–Taylor instability with surface tension in two dimensions

In this paper, we study the long-time evolutions of the single- and multi-mode Rayleigh–Taylor instability with surface tension in two dimensions by using the vortex sheet model. Applying a spectrally accurate numerical method, we investigate the effects of surface tension and density jump on the instability in various regimes of parameters. Complex phenomena of pinching, capillary waves, elongation, and roll-up appear at the interfaces. For a single-mode interface, surface tension retards the growths of bubble and spike. The effect of surface tension on the bubble and spike velocity is generally small but is large for a spike of an infinite density ratio. For multi-mode interfaces, we focus on an infinite density ratio. We show that bubbles grow with the scaling law h=αAgt2 even in the presence of surface tension, while spikes follow the scaling law weakly. It is found that both the growth rates of bubbles and spikes decrease with surface tension and the growth rate of spikes decreases larger than that of bubbles. The growth rate of the bubble front is in agreements with results of previous numerical simulations and experiments.

Near-wall flow response to large air bubbles rising in inclined water channels

The two-strip electrodiffusion probe is employed to investigate the wall shear rate induced by large air bubbles rising in stagnant or coflowing water within inclined rectangular channels. Synchronized video recordings of bubble movements captured by a high-speed camera provide additional information on the bubble shapes and terminal velocities. The measurements are carried-out in a channel with easily adaptable geometry (three heights and various widths) over a wide range of operation parameters (air volumes and liquid velocities) and inclination angles (from horizontal to vertical arrangement). The main objective of this experimental study is to elucidate the influence of individual operating parameters on the bubble-induced wall shear rate. The typical profile of wall shear rate measured at the center of a flat channel can be characterized by a positive peak at the bubble front location, a negative plateau corresponding to the reverse flow in a liquid film around the bubble, and highly fluctuating values in a wake behind the bubble. Just as the large bubbles in flat channels exhibit a close similarity in their frontal shapes, so do the wall shear rate profiles induced by differently sized bubbles. The magnitude and profile of measured wall shear rate is found to be controlled primarily by the distance between two opposite walls squeezing the rising bubble, thus in flat channels by the channel height. By contrast, widening the channel has no significant effect, even though it contributes to a significant increase in the bubble rise velocity. When the channel is tilted, the rising bubbles are pushed towards the roof wall and thus two distinct wall shear rate profiles are measured at the opposite walls of the channel. The liquid coflow then contributes positively not only to the bubble velocity but also to the magnitude of wall shear rate in the near-wall flow region.

Effect of surface tension on late-time growth of high-Reynolds-number Rayleigh-Taylor instability

In this paper, we numerically investigate the late-time growth of high-Reynolds-number single-mode Rayleigh-Taylor instability in a long pipe by using an advanced phase-field lattice Boltzmann multiphase method. We mainly analyze the influence of surface tension on interfacial dynamic behavior and the development of the bubble front and spike front. The numerical experiments indicate that increasing surface tension can significantly reduce the complexity of formed interfacial structure and also prevents the breakup of phase interfaces. The interface patterns in the instability process cannot always preserve the symmetric property under the extremely small surface tension, but they do maintain the symmetries with respect to the middle line as the surface tension is increased. We also report that the bubble amplitude first increases then decreases with the surface tension. There are no obvious differences between the curves of spike amplitudes for low surface tensions. However, when the surface tension increases to a critical value, it can slow down the spike growth significantly. When the surface tension is lower than the critical value, the development of the high-Reynolds-number Rayleigh-Taylor instability can be divided into four different stages, i.e. the linear growth, saturated velocity growth, reacceleration, and chaotic mixing. The bubble and spike velocities at the second stage show good agreement with those from the modified potential flow theory that takes the surface tension effect into account. After that, the bubble front and spike front are accelerated due to the formation of Kelvin-Helmholtz vortices in the interfacial region. At the late time, the bubble velocity and spike velocity become unstable and slightly fluctuate over time. To determine the nature of the late-time growth, we also measure the bubble and spike normalized accelerations at various interfacial tensions and Atwood numbers. It is found that both the spike and bubble growth rates first increase then decrease with the surface tension in general. Finally, we deduce a theoretical formula for the critical surface tension, below which the Rayleigh-Taylor instability takes place and above which tension it does not occur. It is shown that the critical surface tension increases with the Atwood number and also the numerical predictions by the lattice Boltzmann method are also in accord well with the theoretical results.

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

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

Bubble dynamics of Rayleigh–Taylor flow

A flow of semi-bounded Rayleigh–Taylor instability (SB-RTI) is constructed and simulated to understand the bubble dynamics of the multi-mode Rayleigh–Taylor mixing (MM-RTM). SB-RTI is similar to the well-known single-mode Rayleigh–Taylor instability (SM-RTI), and it acts as a bridge from SM-RTI to MM-RTM. This idea is inspired by Meshkov’s recent experimental observation on the structure of the mixing zone of MM-RTM [E. E. Meshkov, J. Exp. Theor. Phys. 126, 126–131 (2018)]. We suppose that the bubble mixing zone consists of two parts, namely, the turbulent mixing zone at the center and the laminar-like mixing zone nearby the edge. For the latter, the bubble fronts are situated in an environment similar to that of SM-RTI bubbles in the potential flow stage, but with a much looser environment between neighboring bubbles. Therefore, a semi-bounded initial perturbation is designed to produce a bubble environment similar to that in MM-RTM. A non-dimensional potential speed of FrpSB≈0.63 is obtained in SB-RTI, which is larger than that of FrpSM=0.56 in SM-RTI. Combining this knowledge and the widely reported quadratic growth coefficient of αb ≈ 0.025 in the short-wavelength MM-RTM, we derive β ≡ D(t)/hb(t) ≈ (1 + A)/4. This relation is consistent with the MM-RTM simulations from Dimonte et al. [Phys. Fluids 16, 1668–1693 (2004)]. The current three-dimensional and previous two-dimensional results [Zhou et al., Phys. Rev. E 97, 033108 (2018)] support a united mechanism of bubble dynamics in short-wavelength MM-RTM.

Phase-Field Modeling of Microstructure Evolution in the Presence of Bubble During Solidification

Simulation of the solid–liquid–gas interaction during solidification is challenging due to the presence of complex phase interfaces, bubble deformation, and high liquid/gas density ratio. In this work, a hybrid phase-field lattice-Boltzmann (PFLB) approach, together with a parallel and adaptive-mesh-refinement (Para-AMR) algorithm, is developed to model interactions between the gas bubble and solid growth front during solidification. The solid growth and bubble evolution are solved by the phase-field method. Both melt flow and bubble movement are determined by a kinetic-based lattice-Boltzmann model. Bubble dynamics during alloy solidification is modeled and compared with experiments, and a good agreement is achieved for various solid/liquid interfaces including planar, cellular, and dendritic interfaces. Results show that the effect of the bubble on solid array is dependent on the solid/liquid interface morphology, bubble size, and relative position between the bubble center and dendritic tip. Two interaction mechanisms, including engulfment and entrapment, are compared, and the difference is caused mainly by the redistribution of solute. The interaction mechanism between the rising multibubbles with large deformation and the dendritic array is also discussed.

Split radiographic tracer technique to measure the full width of a high energy density mixing layer

We describe a new radiography–based technique for measuring the width of the mixing layer that develops when high–energy–density (HED) fluids of different density mix at an interface. In a traditional radiography target, the denser material includes an embedded, density–matched, high opacity, tracer layer to focus the radiograph on a 2D slice of the 3D flow field. The high opacity layer enhances the contrast between the dense and light materials that permits a clear identification of the spike front, i.e. penetration of the dense material into the light material, but obscures the bubble front, i.e. penetration of the light material into the heavy when the fluids are highly interpenetrated, as in a turbulent mixing layer. On the other hand, removing the tracer layer makes it difficult to identify the interface at all, due to poor contrast and an increased susceptibility to edge effects. Our solution is a split tracer approach where half the target uses the traditional geometry while the other half utilizes a special tracer layer in the light material to produce a radiograph with inverse x-ray opacity characteristics when backlit at a specified x–ray energy. Hydrodynamic equivalency is maintained between the two halves of the target. By making a single target with the traditional and inverse material pairs set side-by-side, we are able to simultaneously measure the penetration of bubbles and spikes in a deeply nonlinear flow, yielding the full mix width. We discuss this new target concept and present our first experiments at the National Ignition Facility (NIF) demonstrating the viability of this technique.

Direct numerical simulations of multi-mode immiscible Rayleigh-Taylor instability with high Reynolds numbers

In this paper, we conduct the high-resolution direct numerical simulations of multimode immiscible Rayleigh-Taylor instability (RTI) with a low Atwood number (At = 0.1) using an improved phase field lattice Boltzmann method. The effect of the Reynolds number on the evolutional interfacial dynamics and bubble/spike amplitudes is first investigated by considering its wide range, from 100 up to a high value of 30 000. The numerical results show that, for sufficiently large Reynolds numbers, a sequence of distinguishing stages in the immiscible RTI can be observed, which includes the linear growth, saturated velocity growth, and chaotic development stages. At the late stage, the RTI induces a complex topology structure of the interface and a mass of dissociative drops can be significantly observed in the system. The accelerations of the bubble and spike front are also measured, and it is reported that their normalized values at the late time are, respectively, approximate to the constant values of around 0.025 and 0.027, exhibiting a terminally quadratic growth. As the Reynolds number is reduced to small ones, the multiple disturbances of the RTI are found to merge into a larger one at the initial stage. Then, the evolutional interfaces display the patterns familiar from the single-mode RTI. The phase interfaces in the whole process become very smooth without the appearance of the breakup phenomenon, and the spike and bubble velocities at the late time approach constant values. Furthermore, we also analyze the effects of the initial conditions in terms of the perturbation wavelength and amplitude, and it is found that the instability undergoes a faster growth at the intermediate stage for a larger wavelength, while the late-time bubble and spike growth rates are insensitive to the changes of the initially perturbed wavelength and amplitude.

Bubble Migration Velocity in a Uniform Pore Network

Gas bubbles can be generated naturally or introduced artificially in porous media. Gas bubble migration through porous media governs the rate of gas emission to the atmosphere as well as the hydraulic and mechanical properties of sediments. The migration of air bubbles through water-wet porous media of uniform geometry was studied using a glass micromodel. Experiments were conducted to measure the velocity of bubbles of various lengths rising in a glass micromodel saturated with different test liquids and varying elevation angles. The results showed a linear dependency of the average bubble velocity on the bubble length and the sine of inclination angle of the micromodel. Comparisons were made using experimental data for air bubbles rising in kerosene, Soltrol 170 and dyed white oil. The effective permeability of the micromodel for the gas bubble, Kg, was calculated for different systems at different inclination angles, assuming that the effective length for viscous dissipation is equal to the initial static bubble length. It was found that the calculated permeability of the medium for gas bubbles had an increasing trend with increasing the bubble length. To visualize the periodic nature of the flow of rising bubbles in a porous medium, the motion of the air bubbles in white oil was video recorded by a digital camera, reviewed and analyzed using PowerDVDTM11 software. The bubble shape, exact positions of the bubble front and bubble tail during motion and, hence, the dynamic bubble length were determined through image analysis. Numerical simulation was performed by modifying an existing simulation code for the rise velocity of a gas bubble and the induced pressure field while it migrates through the pore network. The results showed that the rise velocity of a gas bubble is affected by the grid size of the pore network in the direction perpendicular to the bubble migration. The findings of this study can have important implications for studies on the migration of injected gas bubbles in geoenvironmental applications, as well as fundamental studies on bubble transport and behavior in porous media.

Phase-field method based on discrete unified gas-kinetic scheme for large-density-ratio two-phase flows.

In this paper, a phase-field method under the framework of discrete unified gas-kinetic scheme (DUGKS) for incompressible multiphase fluid flows is proposed. Two kinetic models are constructed to solve the conservative Allen-Cahn equation that accounts for the interface behavior and the incompressible hydrodynamic equations that govern the flow field, respectively. With a truncated equilibrium distribution function as well as a temporal derivative added to the source term, the macroscopic governing equations can be exactly recovered from the kinetic models through the Chapman-Enskog analysis. Calculation of source terms involving high-order derivatives existed in the quasi-incompressible model is simplified. A series of benchmark cases including four interface-capturing tests and four binary flow tests are carried out. Results compared to that of the lattice Boltzmann method (LBM) have been obtained. A convergence rate of second order can be guaranteed in the test of interface diagonal translation. The capability of the present method to track the interface that undergoes a severe deformation has been verified. Stationary bubble and spinodal decomposition problems, both with a density ratio as high as 1000, are conducted and reliable solutions have been provided. The layered Poiseuille flow with a large viscosity ratio is simulated and numerical results agree well with the analytical solutions. Variation of positions of the bubble front and spike tip during the evolution of Rayleigh-Taylor instability has been predicted precisely. However, the detailed depiction of complicated interface patterns appearing during the evolution process is failed, which is mainly caused by the relatively large numerical dissipation of DUGKS compared to that of LBM. A high-order DUGKS is needed to overcome this problem.

Effect of gas–liquid ratio on the wall shear stress in slug flow in capillary membranes

AbstractThe membrane processes generally suffer from the fouling caused by the deposits at the membrane surface and membrane pores. In recent years, gas–liquid flow has been shown to be an effective method of membrane fouling prevention. Among the different flow regimes that occur during gas–liquid flow through membrane capillaries, slug flow has been observed to be the most effective for enhancement of permeate flux. The shearing caused by the fluid on the membrane wall is the primary factor causing fouling removal. Previous studies in the slug flow regime suggest that the major contribution to the wall shear stress comes from the bubble front and rear regions and the contribution from the constant film thickness region in the middle is negligible. Therefore, the average wall shear stress in the slug flow regime is dependent on the bubble length. In this work, two‐phase gas–liquid flow in a capillary has been modeled computationally to understand the effect of bubble length on the wall shear stress. Further, the effect of liquid viscosity on the wall shear stress has also been studied for capillary numbers ranging from 0.0037 to 0.098. The volume‐of‐fluid method has been employed to capture the gas–liquid interface between the two phases. The results have been compared with a simple phenomenological model for wall shear stress available in literature and found to be in good agreement for long Taylor bubbles.

Effects of radiation reaction on laser proton acceleration in the bubble regime

We investigated laser proton acceleration in the bubble regime when radiation reaction (RR) effects become non-negligible. By using particle-in-cell simulations, it is shown that in addition to the bubble field, the RR trapped electrons form another charge-separation field, leading to fast acceleration of the background protons at the early stage. However, for insufficient laser intensities, the reduced bubble field and acceleration length originating from the laser depletion by gamma-photon emission do not allow for trapping and further acceleration of the protons. The final proton energy is significantly smaller than the one when RR is not considered. This effect can be mitigated by tuning the peak laser intensity (hence the pulse duration) for certain laser energy and plasma density. By increasing the laser intensity (shortening the pulse duration), we found that protons pre-accelerated by the RR-induced charge separation field gain enough momenta such that they are picked-up by the bubble field and continuously accelerated. In this case, the bubble field is also strong enough to trap protons located in the bubble front. Eventually, two groups of protons are effectively accelerated, resulting in a bump in the proton spectrum. These results can be used to design the future proton acceleration experiments in upcoming 100 PW laser facilities.

Modal model mean field self-similar solutions to the asymptotic evolution of Rayleigh-Taylor and Richtmyer-Meshkov instabilities and its dependence on the initial conditions

The evolution of Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities for incompressible and immiscible fluids and their dependence on the initial perturbation spectrum is evaluated using a new mean field formulation of the Haan-Ofer-Shvarts mode coupling model. The height of the lighter fluid bubbles penetrating into the denser fluid is shown to reach asymptotic, universal, self-similar behavior when the initial spectrum is dominated by short wavelengths and at least 3–4 mode coupling generations have occurred. For RT, the model yields h=αRTAgt2 for the bubble front penetration height, in good agreement with experimental data and 3D numerical simulations for various initial conditions. For RM, the lack of a natural length scale leads to a 2nd type self-similar solution h=αRMtθ and θ is rigorously determined from a detailed solution of the model equation, while αRM retains knowledge of the initial spectrum. The value of θRM in two dimensions is θ2D = 2/5, consistent with the Alon-Shvarts bubble-merger model and numerical simulations, and in three dimensions, it is θ3D = 1/3. We find that the smaller value θ3D ∼ 0.25 ± 0.05 obtained in numerical simulations and experiments [Dimonte and Schneider, Phys. Fluids 12, 304 (2000)] results from the lack of enough mode coupling generations needed to reach the RM asymptotic self-similar stage. The feasibility of a true self-similar RM experiment on NIF is discussed.

Richtmyer-Meshkov unstable dynamics influenced by pressure fluctuations

We theoretically study the effect of pressure fluctuations on the Richtmyer-Meshkov (RM) unstable interface in approximation of ideal incompressible immiscible fluids and two-dimensional flow. Pressure fluctuations are treated as an effective acceleration directed from the heavy to light fluid with inverse square time dependence. The group theory approach is applied to analyze large-scale coherent dynamics, solve the complete set of the governing equations, and find regular asymptotic solutions describing RM bubbles. A strong effect is found, for the first time to our knowledge, of pressure fluctuations on the interface morphology and dynamics. In the linear regime, a nearly flat bubble gets more curved, and its velocity increases for strong pressure fluctuations and decreases otherwise. In the nonlinear regime, solutions form a one-parameter family parameterized by the bubble front curvature. For the fastest stable solution in the family, the RM bubble is curved for strong pressure fluctuations and is flattened otherwise. The flow is characterized by the intense motion of the fluids in the vicinity of the interface, effectively no motion away from the interface, and presence of shear at the interface leading to formation of smaller scale vortical structures. Our theoretical results agree with and explain existing experiments and simulations and identify new qualitative and quantitative characteristics to evaluate the strength of pressure fluctuations in experiments and simulations.