We seek to understand the distribution of irreversible energy conversions (mixing efficiency) between quiescent initial and final states in a miscible Rayleigh-Taylor driven system. The configuration we examine is a Rayleigh-Taylor unstable interface sitting between stably stratified layers with linear density profiles above and below. Our experiments in brine solution measure vertical profiles of density before and after the unstable interface is allowed to relax to a stable state. Our analysis suggests that less than half the initially available energy is irreversibly released as heat due to viscous dissipation, while more than half irreversibly changes the probability density function of the density field by scalar diffusion and therefore remains as potential energy, but in a less useful form. While similar distributions are observed in Rayleigh-Taylor driven mixing flows between homogeneous layers, our new configuration admits energetically consistent end-state density profiles that span all possible mixing efficiencies, ranging from all available energy being expended as dissipation, to none. We present experiments that show that the fluid relaxes to a state with a significantly lower mixing efficiency than the value for ideal mixing in this configuration, and deduce that this mixing efficiency more accurately characterizes Rayleigh-Taylor driven mixing than previous measurements. We argue that the physical mechanisms intrinsic to Rayleigh-Taylor instability are optimal conditions for mixing, and speculate that we have observed an upper bound to fluid mixing in general.

We describe numerical simulations of the miscible Rayleigh-Taylor (RT) instability driven by a complex acceleration history, g(t), with initially destabilizing acceleration, g > 0, an intermediate stage of stabilizing deceleration, g < 0, and subsequent destabilizing acceleration, g > 0. Initial perturbations with both single wavenumber and a spectrum of wavenumbers (leading to a turbulent front) have been considered with these acceleration histories. We find in the single-mode case that the instability undergoes a so-called phase inversion during the first acceleration reversal from g > 0 to g < 0. If the zero-crossing of g(t) occurs once the instability growth has reached a state of nonlinear saturation, then hitherto rising bubbles and falling spikes reverse direction and collide, causing small-scale structures to emerge and enhancing molecular mixing in the interfacial region. Beyond the second stationary point of g(t) where once again g > 0, the horizontal mean density profile becomes RT-unstable and the interfacial region continues to enlarge. Secondary Kelvin-Helmholtz-unstable structures on the near-vertical sheared edges of the primary bubble have an Atwood-number-dependent influence on the primary RT growth rate. This Atwood number dependence appears to occur because secondary instabilities strongly promote mixing, but the formation of these secondary structures is suppressed at large density differences. For multi-mode initial perturbations, we have selected an initial interfacial amplitude distribution h0 (λ) that rapidly achieves a self-similar state during the initial g > 0 acceleration. The transition from g > 0 to g < 0 induces significant changes in the flow structure. As with the single-mode case, bubbles and spikes collide during phase inversion, though in this case the interfacial region is turbulent, and the region as a whole undergoes a period of enhanced structural breakdown. This is accompanied by a rapid increase in the rate of molecular mixing, and increasing isotropy within the region. During the final stage of g > 0 acceleration, self-similar RT mixing re-emerges, together with a return to anisotropy. We track several turbulent statistical quantities through this complex evolution, which we present as a resource for the validation and refinement of turbulent mix models.

The influence of initial conditions on miscible incompressible baroclinically driven Rayleigh-Taylor instability undergoing non-uniform acceleration is explored computationally using an Implicit Large Eddy Simulation (ILES) technique. We consider the particular case of evolution during multiple reversals of acceleration direction, where the flow is alternately statically stable or unstable. In the unstable phase, the flow is driven by the baroclinic release of potential energy, whereas in the stable phase, work is done against the density stratification with the energy exchange taking place by wave-like mechanisms. These dynamics are fundamentally different; here, we track the evolution of volume-averaged turbulent statistics that are most sensitive to changes in the distribution of spectral power and bandwidth of the initial conditions as the flow alternates between dynamical regimes due to acceleration reversal.3

We present a novel apparatus for generating internal waves of arbitrary size and shape, including both phase-locked and propagating waves. It is an actively driven, flexible "magic carpet" in the base of a tank. Our wave maker is computercontrolled to enable easy configuration. The actuation of a smooth, flexible surface produces clean waveforms with a predictable spectrum, for which we derive a theoretical model. We demonstrate the versatility of our wave maker through an experimental study of linear and nonlinear, isolated, and combined internal waves, including some that are sufficiently nonlinear to break remote from their source.