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.

A perturbation method in which only the most secular terms are retained gives simple results for the weakly nonlinear growth of a single-mode shock-accelerated interface (Vandenboomgaerde et al., 2002). This result can be written as a series in integer powers of time. It can be considered as the Taylor expansion of an analytic function. We believe that an approximation of such a function has been identified; it described the evolution of the instability from linear to intermediate nonlinear regime. Furthermore, this function has no singularity. The relevance of this analytic formula is checked against two-dimensional simulations and experimental data.

The simplified perturbation method of Vandenboomgaerde et al. (2002) is applied to both the Richtmyer–Meshkov and the Rayleigh–Taylor instabilities. This theory is devoted to the calculus of the growth rate of the perturbation of the interface in the weakly nonlinear stage. In the standard approach, expansions appear to be series in time. We build accurate approximations by retaining only the terms with the highest power in time. This simplifies and accelerates the solution. High order expressions are then easily reachable. For the Richtmyer–Meshkov instability, multimode configurations become tractable and the selection mode process can be studied. Inferences for the intermediate nonlinear regime are also proposed. In particular, a class of homothetic configurations is inferred; its validity is verified with numerical simulations even as vortex structures appear at the interface. This kind of method can also be used for the Rayleigh–Taylor instability. Some examples are presented.

Directed energy and turbulence structure are shown to be crucial in understanding the growth of self-similar Rayleigh–Taylor and incompressible Richtmyer–Meshkov turbulent mixing zones. Averaging over the mixing zone is used to analyze the response of a modified k–ε model and a turbulent two-fluid model. Three different transport regimes are then identified by considering self-similar variable acceleration RT flows (SSVARTs), which appear as promising reference flows for model testing.

An accurate turbulent mixing model for gravitationally induced instabilities with arbitrarily variable accelerations has been developed to capture the following physical aspects: (1) directed transport, (2) correct buoyancy forces, (3) turbulence diffusion, and (4) geometrical aspects. We present the two-structure two-fluid two-turbulence concept (2SFK), which consistently answers these requirements by identifying the large-scale transport structures in a statistical approach. An example of a 2SFK-based model is given and applied to the Rayleigh–Taylor case.