Guy Dimonte

A comparative study of the turbulent Rayleigh–Taylor instability using high-resolution three-dimensional numerical simulations: The Alpha-Group collaboration

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 (NS). The perturbations are initialized with only short wavelength modes so that the self-similar evolution (i.e., bubble diameter Db∝amplitude hb) occurs solely by the nonlinear coupling (merger) of saturated modes. After an initial transient, it is found that hb∼αbAgt2, where A=Atwood number, g=acceleration, and t=time. The NS yield Db∼hb/3 in agreement with experiment but the simulation value αb∼0.025±0.003 is smaller than the experimental value αb∼0.057±0.008. By analyzing the dominant bubbles, it is found that the small value of αb can be attributed to a density dilution due to fine-scale mixing in our NS without interface reconstruction (IR) or an equivalent entrainment in our NS with IR. This may be characteristic of the mode coupling limit studied here and the associated αb may represent a lower bound that is insensiti...

Density ratio dependence of Rayleigh-Taylor mixing for sustained and impulsive acceleration histories

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 i...

Richtmyer–Meshkov instability growth: experiment, simulation and theory

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.

On validating an astrophysical simulation code

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 multilayer 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 multilayer 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.

Single‐mode and multimode Rayleigh–Taylor experiments on Nova

Rayleigh–Taylor (RT) experiments have been conducted with planar CH(Br) foils accelerated by x‐ray ablation from a shaped, low adiabat drive. The surface perturbations investigated consisted of single‐mode, two‐mode, and eight‐mode sinusoids. The perturbation evolution begins during the shock transit phase, when perturbations show gradual growth due to Richtmyer–Meshkov‐like dynamics. After shock breakout, the compressed foils accelerate and perturbation growth continues due to the Rayleigh–Taylor instability. Detailed comparisons with simulations indicate that in the linear Rayleigh–Taylor regime, the single‐mode perturbations grow exponentially in time. In the nonlinear regime, the growth slows and the perturbation shape changes from sinusoidal to ‘‘bubble and spike’’ with the appearance of higher Fourier harmonics. In the multimode perturbations, the individual modes grow independently in the linear regime, but become coupled in the nonlinear regime. In addition to the higher harmonics of the individua...

Spanwise homogeneous buoyancy-drag model for Rayleigh–Taylor mixing and experimental evaluation

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.

Nonlinear evolution of the Rayleigh–Taylor and Richtmyer–Meshkov instabilities

Scaled experiments on the nonlinear Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities are described for two limiting conditions. First, at high Reynolds number, the mixing layer is found to grow self-similarly ∼αiAgt2 for a constant acceleration and as a power law tθi for an impulsive acceleration g=Uδ(t). The growth coefficients αi and exponents θi are measured over a comprehensive range of Atwood number A. Second, with non-Newtonian materials, the critical wavelength and amplitude for RT instability associated with the shear modulus and tensile yield of the material is observed over a variety of conditions. The results are applied to naturally occurring supernova explosions and volcanic islands.

Richtmyer–Meshkov instability with strong radiatively driven shocks

The Richtmyer–Meshkov instability is investigated with strong radiatively driven shocks (Mach≳20, 5×compression) using the Nova laser. The target consists of a solid density ablator and lower‐density plastics (Atwood number A<0) in planar geometry to facilitate in‐flight radiographic diagnosis. Perturbations η=η0 cos kx are imposed at the interface to seed the instability. The experiments agree with full hydrodynamic simulations over a wide variety of conditions. For small initial amplitudes ‖A‖kη0<1, the growth rate agrees with a linear impulsive model using the average of the pre‐ and post‐shock initial amplitudes. For ‖A‖kη0≳1, the growth rate is limited to the difference between the transmitted shock speed and the interface speed.

A numerical study of the influence of initial perturbations on the turbulent Rayleigh-Taylor instability

The effect of initial conditions on the growth rate of turbulent Rayleigh–Taylor (RT) mixing has been studied using carefully formulated numerical simulations. A monotone integrated large-eddy simulation (MILES) using a finite-volume technique was employed to solve the three-dimensional incompressible Euler equations with numerical dissipation. The initial conditions were chosen to test the dependence of the RT growth coefficient (

K-L turbulence model for the self-similar growth of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities

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