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.

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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.

The self-similar evolution to turbulence of a multi-mode miscible Rayleigh–Taylor (RT) mixing layer has been investigated for Atwood numbers 0.03–0.6, using an air–helium gas channel experiment. Two co-flowing gas streams, one containing air (on top) and the other a helium–air mixture (at the bottom), initially flowed parallel to each other at the same velocity separated by a thin splitter plate. The streams met at the end of the splitter plate, with the downstream formation of a buoyancy unstable interface, and thereafter buoyancy-driven mixing. This buoyancy-driven mixing layer experiment permitted long data collection times, short transients and was statistically steady. Several significant designs and operating characteristics of the gas channel experiment are described that enabled the facility to be successfully run for At ~ 0.6. We report, and discuss, statistically converged measurements using digital image analysis and hot-wire anemometry. In particular, two hot-wire techniques were developed for measuring the various turbulence and mixing statistics in this air–helium RT experiment. Data collected and discussed include: mean density profiles, growth rate parameters, various turbulence and mixing statistics, and spectra of velocity, density and mass flux over a wide range of Atwood numbers (0.03 ≤ At ≤ 0.6). In particular, the measured data at the small Atwood number (0.03–0.04) were used to evaluate several turbulence-model constants. Measurements of the root mean square (r.m.s.) velocity and density fluctuations at the mixing layer centreline for the large At case showed a strong similarity to lower At behaviours when properly normalized. A novel conditional averaging technique provided new statistics for RT mixing layers by separating the bubble (light fluid) and spike (heavy fluid) dynamics. The conditional sampling highlighted differences in the vertical turbulent mass flux, and vertical velocity fluctuations, for the bubbles and spikes, which were not otherwise observable. Larger values of the vertical turbulent mass flux and vertical velocity fluctuations were found in the downward-falling spikes, consistent with larger growth rates and momentum of spikes compared with the bubbles.

A new water channel experiment has been used to study turbulent mixing driven by buoyancy, and by combined buoyancy and shear. Density differences were produced by thermal stratification. The experiment was statistically steady, and a space–time transformation in the streamwise direction permitted a continuous study of the mixing evolution. Dye and digitized photographs were used to study the mixing process. An ensemble average of images gave the average mixing layer growth rate and the distribution of light and heavy fluid in the mixing layer. The structure of the early growth of buoyancy dominated mixing and of combined shear and buoyancy mixing is presented. The mixing transition from combined shear and buoyancy mixing to buoyancy dominated mixing occurred at Richardson numbers from −5 to −11. It was found that buoyancy dominated a self-similar mixing stage for the range of flows (ΔU=0 to 2 cm/s) and density differences (Δρ=0.38 to 2.4 kg/m3). Transition to self-similar mixing occurred at a Reynolds number from 670 to 1200. The self-similar mixing width for all tests had a quadratic growth rate with an average acceleration constant of 0.070 and a standard deviation of 0.011.

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.

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A simple experiment to study the mixing of two different density fluids by the Rayleigh–Taylor instability has been performed. Several experiments are reported for nominally one-dimensional homogeneous mixing and for experiments characterized by a large two-dimensional motion superimposed on the mixing process. The one-dimensional experiments show a plane mixing region that expands by Rayleigh–Taylor instabilities. The two-dimensional experiments show a contraction in the width of the mixing interface that is a result of the stretching action of the large-scale motion. Image analysis techniques have been developed to provide quantitative measurements for use in a ‘‘two-fluid’’ model of the mixing phenomena.