We describe the evolution of the large-scale coherent structure of bubbles and spikes in the Richtmyer–Meshkov instability. Our multiple harmonic analysis accounts for a non-local character of the nonlinear dynamics. A new type of the evolution of the bubble front is found. A comparison to so-called “Layzer-type” local models is performed.

Acceleration-driven fluid mixing is studied here from a theoretical point of view. Considerable progress has been achieved in the understanding of mix. Theories of the authors are reviewed that allow prediction of the edge of the mixing zone, in agreement with experimental data. Theories that describe the distribution of masses within the mixing region are also reviewed. The theory we present describes a chunk mix regime, in which two phases are mixed at a chunk level, but for which there is no atomic mixing. Thus the two phases are segregated into disjoint regions of space.

We present a Rayleigh–Taylor mixing rate simulation with an acceleration rate falling within the range of experiments. The simulation uses front tracking to prevent interfacial mass diffusion. We present evidence to support the assertion that the lower acceleration rate found in untracked simulations is caused, at least to a large extent, by a reduced buoyancy force due to numerical interfacial mass diffusion. Quantitative evidence includes results from a time-dependent Atwood number analysis of the diffusive simulation, which yields a renormalized mixing rate coefficient for the diffusive simulation in agreement with experiment. We also present the study of Richtmyer–Meshkov mixing in cylindrical geometry using the front tracking method and compare it with the experimental results.

We present a numerical study to late times of a Richtmyer–Meshkov environment: a weak shock (M = 1.095) interacting with a heavy cylindrical bubble. The bubble interface is modeled as a diffuse interfacial transition layer (ITL) with finite thickness. Our simulation with the piecewise parabolic method (PPM) yields very good agreement in large- and intermediate-scale features with Jacobs' experiment (Jacobs, 1993). We note the primary circulation enhancement deposited baroclinically upon the incident shock wave, and significant secondary baroclinic circulation enhancement, first observed in Zabusky and Zhang (2002). We propose that this vortex-accelerated circulation deposition is universal. These baroclinic processes are mediated by a strong gradient intensification and stretching of the ITL and result in close-lying vortex bilayers (VBLs) and the emergence of vortex projectiles (VPs). These account for the elongated, kidney-shaped morphology of the rolled up bubble domain at late times.

We suggest an easily obtained laboratory configuration to observe jet and vortex flows for the Richtmyer–Meshkov (accelerated inhomogeneous flow) environment. A hemispherical bubble in air with density ratio of 5 is placed against an ideally reflecting wall and struck by a planar shock. This also models a spherical bubble struck symmetrically by two identical approaching shocks, that is, a “reshock” configuration. For all Mach numbers (M = 1.2, 1.5, and 2.0), our axisymmetric simulations show that the heavy hemispherical bubble expands axially away from the wall as a jet, and a weaker vortex ring moves radially along the wall. In addition, when M = 1.5, a ringlike vortex projectile (VP) of small diameter follows closely behind the reflected shock and is associated with its moving triple point. This VP contains an entrained shocklet and quadrupole structure of dilatation. Various methods are applied to quantify the emerging coherent structures.

We have performed simulations of the evolution of the turbulent Rayleigh–Taylor instability with an arbitrary Lagrange–Eulerian code. The problem specification was defined by Dimonte et al. (2003) for the “alpha group” code intercomparison project. Perfect γ = 5/3 gases of densities 1 and 3 g/cm3 are accelerated by constant gravity. The nominal problem uses a 2562 × 512 mesh with initial random multiwavelength interface perturbations. We have also run three-dimensional problems with smaller meshes and two-dimensional (2D) problems of several mesh sizes. Under-resolution lowered linear growth rates of the seed modes to 5-60% of the analytic values, depending on wavelength and orientation to the mesh. However, the mix extent in the 2D simulations changed little with grid refinement. Simulations without interface reconstruction gave penetration only slightly reduced from the case with interface reconstruction. Energy dissipation differs little between the two cases. The slope of the penetration distance versus time squared, corresponding to the α parameter in h = αAgt2, decreases with increasing time in these simulations. The slope, α, is consistent with the linear electric motor data of Dimonte and Schneider (2000), but the growth is delayed in time.

We continue our previous investigations (Yang, Zabusky, & Chern, 1990; Zabusky & Zhang, 2002) of the interaction of a shock with a planar, inclined curtain (slow/fast/slow) to a wider Mach number range (M = 1.5, 2.0, and 5.0) and longer times. In all cases, the generic features may be explained in terms of the opposite-signed vortex layers (deposited by the shock wave), which approach and collide to form a complex vortex bilayer (VBL). At M ≤ 2.0, the VBL traverses the shock tube and eventually collides with the opposite horizontal boundary and evolves into upstream and downstream moving inhomogeneous vortex projectiles (VPs) (Zabusky & Zeng, 1998). This is manifested as early-time “breakthrough” (Yang, Zabusky, & Chern, 1990). During the traversal, we observe and scale a strong secondary baroclinic circulation enhancement. We track and quantify the VPs and show that their velocities compare well to that from a simple vortex model. We also display turbulent domains and a new rapid early time turbulization at M = 5, when the VBL is narrower.

We examine the interaction of both cylindrical and spherical bubbles (2D) and a complex blast wave, which consists of an approaching shock/contact discontinuity/shock (Kang et al., 2001a, 2001b). Such configurations may arise following a supernova explosion, for example, SN 1987A, where a complex blast wave is presently approaching a high density “circumstellar ring” (CR) (Borkowski et al., 1997). Using simulations with the piecewise parabolic method algorithm (Colella & Woodward, 1984), we emphasize the appearance of vortex bilayers, vortex projectiles, and turbulent domains on the downstream and upstream sides of the bubble. We believe that the interfacial deformation of the CR is associated with a strong blast-wave driven accelerated inhomogeneous flow instability in a high density medium and thus will have a different character than the more common planar shock-driven Richtmyer–Meshkov instability.