The turbulent Rayleigh-Taylor instability is investigated in the limit of strong mode-coupling using a variety of high-resolution, multimode, three dimensional numerical simulations ͑NS͒. The perturbations are initialized with only short wavelength modes so that the self-similar evolution ͑i.e., bubble diameter D b ϰamplitude h b) occurs solely by the nonlinear coupling ͑merger͒ of saturated modes. After an initial transient, it is found that h b ϳ␣ b Agt 2 , where AϭAtwood number, gϭacceleration, and tϭtime. The NS yield D b ϳh b /3 in agreement with experiment but the simulation value ␣ b ϳ0.025Ϯ0.003 is smaller than the experimental value ␣ b ϳ0.057Ϯ0.008. By analyzing the dominant bubbles, it is found that the small value of ␣ b can be attributed to a density dilution due to fine-scale mixing in our NS without interface reconstruction ͑IR͒ or an equivalent entrainment in our NS with IR. This may be characteristic of the mode coupling limit studied here and the associated ␣ b may represent a lower bound that is insensitive to the initial amplitude. Larger values of ␣ b can be obtained in the presence of additional long wavelength perturbations and this may be more characteristic of experiments. Here, the simulation data are also analyzed in terms of bubble dynamics, energy balance and the density fluctuation spectra.

The turbulent Rayleigh–Taylor instability is investigated over a comprehensive range of fluid density ratio (R)1.3⩽R⩽50 [0.15⩽A=(R−1)/(R+1)⩽0.96] and different acceleration histories g(t) using the Linear Electric Motor. The mixing layer is diagnosed with backlit photography and laser-induced fluorescence. For a constant acceleration, the bubble (2) and spike (1) amplitudes are found to increase as hi=αiAgt2 with α2∼0.05±0.005 and α1∼α2RDα with Dα∼0.33±0.05. For temporally varying accelerations Ag(t)>0, this can be generalized to hi=2αiAS using S=[∫gdt]2/2 rather than the displacement Z=∫∫gdt′ dt. For impulsive accelerations, S remains constant during the coast phase and the amplitudes obey a power law hi∼tθi with θ2∼0.25±0.05 and θ1∼θ2RDθ with Dθ∼0.21±0.05. These values of Dα and Dθ compare favorably with numerical simulations and mix models. The average diameter at the mixing front for bubbles is found to increase as d2∼h2(1+A)/4 in qualitative agreement with “merger” models, but the associated dhi/dt is two times larger than the terminal velocity of an isolated bubble. The spikes become relatively narrow at large R, yet they still grow as gt2.

Molecular-dynamics simulations are used to investigate temperature relaxation between electrons and ions in a fully ionized, classical Coulomb plasma with minimal assumptions. Recombination is avoided by using like charges. The relaxation rate agrees with theory in the weak coupling limit (g identical with potential/kinetic energy << 1), whereas it saturates at g > 1 due to correlation effects. The "Coulomb log" is found to be independent of the ion charge (at constant g) and mass ratio > 25.

A turbulence model is developed to described the self-similar growth of the Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities. The model describes the dominant eddies in the mixing zone with evolutionary equations for their characteristic dimension L and energy per unit mass K≡V2∕2. The equations are based on the successful buoyancy-drag models for RT and RM flows, but constructed only with local parameters so that it can be applied to multidimensional flows with multiple shells of materials. The model has several unknown coefficients that are determined by comparing analytical and numerical solutions with RT and RM experiments.

We present a case study of validating an astrophysical simulation code. Our study focuses on validating FLASH, a parallel, adaptive-mesh hydrodynamics code for studying the compressible, reactive flows found in many astrophysical environments. We describe the astrophysics problems of interest and the challenges associated with simulating these problems. We describe methodology and discuss solutions to difficulties encountered in verification and validation. We describe verification tests regularly administered to the code, present the results of new verification tests, and outline a method for testing general equations of state. We present the results of two validation tests in which we compared simulations to experimental data. The first is of a laser-driven shock propagating through a multi-layer target, a configuration subject to both Rayleigh-Taylor and Richtmyer-Meshkov instabilities. The second test is a classic Rayleigh-Taylor instability, where a heavy fluid is supported against the force of gravity by a light fluid. Our simulations of the multi-layer target experiments showed good agreement with the experimental results, but our simulations of the Rayleigh-Taylor instability did not agree well with the experimental results. We discuss our findings and present results of additional simulations undertaken to further investigate the Rayleigh-Taylor instability.Comment: 76 pages, 26 figures (3 color), Accepted for publication in the ApJ

A buoyancy-drag model for Rayleigh–Taylor (RT) mixing is developed on the premise that the bubble and spike regions behave as distinct and spanwise homogeneous fluids. Then, mass conservation is applied accross the mixing zone to obtain their average mixture densities dynamically. These are used to explicitly calculate the inertia and buoyancy terms in the evolutionary equation. The only unknown parameter in the model is the Newtonian drag constant C∼2.5±0.6, which is determined from turbulent RT experiments over various Atwood numbers A and acceleration histories g(t). The bubble (i=2) and spike (i=1) amplitudes are found to obey the familiar hi=αiAgt2 for a constant g and hi∼tθi for an impulsive g. For bubbles, both α2 and θ2 are insensitive to A. For the spikes, both α1 and θ1 increase as a power law with the density ratio. However, θ1 is not universal because it depends on the initial value of h1/h2.

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Richtmyer–Meshkov instability is investigated for negative Atwood number and two-dimensional sinusoidal perturbations by comparing experiments, numerical simulations and analytic theories. The experiments were conducted on the NOVA laser with strong radiatively driven shocks with Mach numbers greater than 10. Three different hydrodynamics codes (RAGE, PROMETHEUS and FronTier) reproduce the amplitude evolution and the gross features in the experiment while the fine-scale features differ in the different numerical techniques. Linearized theories correctly calculate the growth rates at small amplitude and early time, but fail at large amplitude and late time. A nonlinear theory using asymptotic matching between the linear theory and a potential flow model shows much better agreement with the late-time and large-amplitude growth rates found in the experiments and simulations. We vary the incident shock strength and initial perturbation amplitude to study the behaviour of the simulations and theory and to study the effects of compression and nonlinearity.