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 self-similar evolution to turbulence of a multi-mode Rayleigh-Taylor mix at small density differences (A t ∼ 7.5 × 10 −4), is investigated through particle image velocimetry (PIV), and high-resolution thermocouple measurements. The density difference has been achieved through a temperature difference in the fluid. Cold fluid enters above the hot in a closed channel to form an unstable interface. This buoyancy-driven mixing experiment allows for long data collection times, short transients, and is statistically steady. First-, second-, and third-order statistics with spectra of velocity and temperature fields are presented. Analysis of the measurements has shed light on the structure of mixing as it develops to a self-similar regime in this flow. The onset of selfsimilarity is marked by the development of a self-preserving form of the temperature spectra, and the collapse of velocity profiles expressed in self-similar units. Vertical velocity fluctuations dominate horizontal velocity fluctuations in this experiment, with a ratio approaching 2:1 in the self-similar regime. This anisotropy extends to the Taylor microscales that undergo differential straining in the direction of gravity. Up to two decades of velocity spectra development, and four decades of temperature spectra, have been captured from the experiment. The velocity spectra consist of an inertial range comprised of anisotropic vertical and horizontal velocity fluctuations, and a more isotropic dissipative range. Buoyancy forcing occurs across the spectrum of velocity and temperature scales, but was not found to affect the structure of the spectra, resulting in a −5/3 slope, similar to other canonical turbulent flows. A scaling argument is presented to explain this observation. The net kinetic energy dissipation, as the flow evolves from an initial state to a final self-similar state was measured to be 49% of the accompanying loss in potential energy, and is in close agreement with values obtained from three-dimensional numerical simulations.

Turbulent Richtmyer-Meshkov instability (RMI) is investigated through a series of high resolution three dimensional smulations of two initial conditions with eight independent codes. The simulations are initialised with a narrowband perturbation such that instability growth is due to non-linear coupling/backscatter from the energetic modes, thus generating the lowest expected growth rate from a pure RMI. By independently assessing the results from each algorithm, and computing ensemble averages of multiple algorithms, the results allow a quantification of key flow properties as well as the uncertainty due to differing numerical approaches. A new analytical model predicting the initial layer growth for a multimode narrowband perturbation is presented, along with two models for the linear and non-linear regime combined. Overall, the growth rate exponent is determined as θ = 0.292 ± 0.009, in good agreement with prior studies; however, the exponent is decaying slowly in time. Also, θ is shown to be relatively insensitive to the choice of mixing layer width measurement. The asymptotic integral molecular mixing measures Θ = 0.792 ± 0.014, Ξ = 0.800±0.014 and Ψ = 0.782±0.013 which are lower than some experimental measurements but within the range of prior numerical studies. The flow field is shown to be persistently anisotropic for all algorithms, at the latest time having between 49% and 66% higher kinetic energy in the shock parallel direction compared to perpendicular and does not show any return to isotropy. The plane averaged volume fraction profiles at different time instants collapse reasonably well when scaled by the integral width, implying that the layer can be described by a single length scale and thus a single θ. Quantitative data given for both ensemble averages and individual algorithms provide useful benchmark results for future research.

The nonlinear evolution of the Richtmyer-Meshkov ͑RM͒ instability is investigated using numerical simulations with the FLASH code in two dimensions. The purpose of the simulations is to develop an empirical nonlinear model of the RM instability that is applicable to inertial confinement fusion ͑ICF͒ and ejecta formation, namely, at large Atwood number A and scaled initial amplitude kh o ͑k ϵ wave number͒ of the perturbation. The FLASH code is first validated with a variety of RM experiments that evolve well into the nonlinear regime. They reveal that bubbles stagnate when they grow by an increment of 2 / k and that spikes accelerate for A Ͼ 0.5 due to higher harmonics that focus them. These results are then compared with a variety of nonlinear models that are based on potential flow. We find that the models agree with simulations for moderate values of A Ͻ 0.9 and kh o Ͻ 1, but not for the larger values that characterize ICF and ejecta formation. We thus develop a new nonlinear empirical model that captures the simulation results consistent with potential flow for a broader range of A and kh o . Our hope is that such empirical models concisely capture the RM simulations and inspire more rigorous solutions.

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 (α b ) and the self-similar parameter (β b = λ b /h b ) on (i) the amplitude, (ii) the spectral shape, (iii) the longest wavelength imposed, and (iv) mode-coupling effects. With long wavelengths present in the initial conditions, α b was found to increase logarithmically with the initial amplitudes, while β b is less sensitive to amplitude variations. The simulations are in reasonable agreement with the predictions for α b from a recently proposed model, but not for β b . In the opposite limit where mode-coupling dominates, no such dependence on initial amplitudes is observed, and α b takes a universal lower-bound value of ∼ 0.03 ± 0.003. This may explain the low values of α b reported by most numerical simulations that are initialized with annular spectra of short-wavelength modes and hence evolve purely through mode-coupling. Small-scale effects such as molecular mixing and kinetic energy dissipation showed a weak dependence on the structure of initial conditions. Initial density spectra with amplitudes distributed as k 0 , k −1 and k −2 were used to investigate the role of the spectral slopes on the development of turbulent RT mixing. Furthermore, in a separate study, the longest wavelength imposed in the initial wavepacket was also varied to determine its effect on α b . It was found that the slopes of the initial spectra, and the longest wavelength imposed had little effect on the RT growth parameters.