Experimental investigation of Rayleigh–Taylor mixing at small Atwood numbers

Abstract

The self-similar evolution to turbulence of a multi-mode Rayleigh–Taylor mix at small density differences ($A_{t} \sim 7.5 \times 10^{ - 4}$), 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 self-similarity 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.