Experimental assessment of mixing layer scaling laws in Rayleigh-Taylor instability

We assess experimentally the scaling laws that characterize the mixing region produced by the Rayleigh-Taylor instability in a confined porous medium. We aim at verifying the existence of a superlinear scaling for the growth of the mixing region, as was observed in recent two-dimensional simulations. The configuration consists of a Hele-Shaw cell and a heavy fluid layer overlying a lighter fluid layer, initially separated by a horizontal, flat interface. When perturbations of the concentration field occur, convective mixing is produced: Perturbations grow and evolve into large finger-like convective structures that control the transition from the initial diffusion-dominated phase to the subsequent convection-dominated phase. As the flow evolves, diffusion acts to reduce local concentration gradients across the interface of the fingers. We employ an optical method to obtain high-resolution measurements of the density fields and we perform experiments for values of the Rayleigh-Darcy number sufficiently large to exhibit all the flow phases, which we characterize via the mixing length, i.e., the extension of the mixing region. We confirm that the growth of the mixing length during the convection-dominated phase follows the superlinear scaling predicted by previous simulations.