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.