Efficient mixing in stratified flows: experimental study of a Rayleigh–Taylor unstable interface within an otherwise stable stratification

Boussinesq salt-water laboratory experiments of Rayleigh–Taylor instability (RTI) can achieve mixing efficiencies greater than 0.75 when the unstable interface is confined between two stable stratifications. This is much greater than that found when RTI occurs between two homogeneous layers when the mixing efficiency has been found to approach 0.5. Here, the mixing efficiency is defined as the ratio of energy used in mixing compared with the energy available for mixing. If the initial and final states are quiescent then the mixing efficiency can be calculated from experiments by comparison of the corresponding density profiles. Varying the functional form of the confining stratifications has a strong effect on the mixing efficiency. We derive a buoyancy-diffusion model for the rate of growth of the turbulent mixing region, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\dot{h} = 2 \sqrt{\alpha A g h}$ (where $A = A(h)$ is the Atwood number across the mixing region when it extends a height $h$, $g$ is acceleration due to gravity and $\alpha $ is a constant). This model shows good agreement with experiments when the value of the constant $\alpha $ is set to 0.07, the value found in experiments of RTI between two homogeneous layers (where the height of the turbulent mixing region increases as $h =\alpha A g t^2$, an expression which is equivalent to that derived for $\dot{h}$).