We describe numerical simulations of the miscible Rayleigh-Taylor (RT) instability driven by a complex acceleration history, g(t), with initially destabilizing acceleration, g > 0, an intermediate stage of stabilizing deceleration, g < 0, and subsequent destabilizing acceleration, g > 0. Initial perturbations with both single wavenumber and a spectrum of wavenumbers (leading to a turbulent front) have been considered with these acceleration histories. We find in the single-mode case that the instability undergoes a so-called phase inversion during the first acceleration reversal from g > 0 to g < 0. If the zero-crossing of g(t) occurs once the instability growth has reached a state of nonlinear saturation, then hitherto rising bubbles and falling spikes reverse direction and collide, causing small-scale structures to emerge and enhancing molecular mixing in the interfacial region. Beyond the second stationary point of g(t) where once again g > 0, the horizontal mean density profile becomes RT-unstable and the interfacial region continues to enlarge. Secondary Kelvin-Helmholtz-unstable structures on the near-vertical sheared edges of the primary bubble have an Atwood-number-dependent influence on the primary RT growth rate. This Atwood number dependence appears to occur because secondary instabilities strongly promote mixing, but the formation of these secondary structures is suppressed at large density differences. For multi-mode initial perturbations, we have selected an initial interfacial amplitude distribution h0 (λ) that rapidly achieves a self-similar state during the initial g > 0 acceleration. The transition from g > 0 to g < 0 induces significant changes in the flow structure. As with the single-mode case, bubbles and spikes collide during phase inversion, though in this case the interfacial region is turbulent, and the region as a whole undergoes a period of enhanced structural breakdown. This is accompanied by a rapid increase in the rate of molecular mixing, and increasing isotropy within the region. During the final stage of g > 0 acceleration, self-similar RT mixing re-emerges, together with a return to anisotropy. We track several turbulent statistical quantities through this complex evolution, which we present as a resource for the validation and refinement of turbulent mix models.

Previous work employed Richtmyer-Meshkov theory to describe the development of spikes and bubbles from shocked sinusoidal surfaces. Here, we discuss the effects of machining different two-dimensional shaped grooves in copper and examine the resulting flow of the material after being shocked into liquid on release. For these simulations, a high performance molecular dynamics code, SPaSM, was used with machined grooves of kh0 = 1 and kh0 = 1/8, where 2h0 is the peak-to-valley height of the perturbation with wavelength λ, and k = 2π/λ. The surface morphologies studied include a Chevron, a Fly-Cut, a Square-Wave, and a Gaussian. We describe extensions to an existing ejecta source model that better captures the mass ejected from these surfaces. We also investigate the same profiles at length scales of order 1 cm for an idealized fluid equation of state using the FLASH continuum hydrodynamics code. Our findings indicate that the resulting mass can be scaled by the missing area of a sinusoidal curve with an effective wavelength, λeff, that has the same missing area. Our extended ejecta mass formula works well for all the shapes considered and captures the corresponding time evolution and total mass.

From nonlinear models and direct numerical simulations we report on several new findings of relevance to the single-mode Rayleigh-Taylor (RT) instability driven by time-varying acceleration histories. The incompressible, Direct Numerical Simulations (DNS) were performed in two-and three-dimensions, and at a range of density ratios of the fluid combinations (characterized by the Atwood number). We investigated several acceleration histories, including acceleration profiles of and with corresponding 3D drag buoyancy model solutions derived in this article. Our generalization of the RT problem to study variable g(t) affords us the opportunity to investigate the appropriate scaling for bubble and spike amplitudes under these conditions. We consider two candidates, the displacement Z and width s 2 , but find the appropriate scaling is dependent on the density ratios between the fluids -at low density ratios, bubble and spike amplitudes are explained by both s 2 and Z, while at large density differences the displacement collapses the spike data. Finally, for all the acceleration profiles studied here, spikes enter a free-fall regime at lower Atwood numbers than predicted by all the models.2

We report on modifications to the widely used astrophysical code, FLASH (Fryxell, Olson et al. 2000) that enable accurate simulations of chemically reacting flows with heat addition. The enhancements to FLASH include the implementation of extensive Hydrogen-air and Methaneair chemistry through multiple, detailed mechanisms (Smooke 1991; Katta and Roquemore 1995; Mueller, Kim et al. 1999; Billet 2005), accomplished by building on the existing infrastructure of nuclear reaction network solvers. The chemical reaction network is represented as a system of coupled ODEs, that are then solved either through the Kaps-Rentrop (Rosenbrok) method(Kaps and Rentrop 1979) or the Bader-Deuflhard method (Bader and