Mixing efficiency in high-aspect-ratio Rayleigh–Taylor experiments

Abstract

High-Reynolds-number turbulence generated by Rayleigh–Taylor instability is known to be much more efficient at mixing density-stratified fluids than mixing driven by most other mechanisms. We demonstrate here that the final state of the instability in a high-aspect-ratio environment is uniform, corresponding to the maximum mixing efficiency possible. The efficiency of the mixing appears to be constant throughout the evolution of the flow, despite the flow changing from being inertially dominated with a high-Reynolds-number initial growth of the mixing zone, to a viscously dominated late-time decay. The initial growth, in which vertical transport takes the form of a turbulent diffusion, is characterized by a t2∕5 power law, indicating that the diffusivity is not constant but rather decreases as the strength of the unstable density gradient driving the flow decreases. As the unstable stratification is reduced, inertia begins to play a lesser role with molecular viscosity taking over the controlling dynamics, but with vertical transport still dominated by parcels of fluid needing to pass around many vortexlike structures during the exponential decay toward the well-mixed final state.