Dimensional transition in Darcy-Rayleigh-Taylor mixing

When a fluid is confined in a thin layer, it undergoes a dramatic change in its dynamical and/or statistical properties, which occurs when the confining scale is of the order of some characteristic scale of the flow. Here we study this dimensional transition in the framework of Rayleigh-Taylor mixing in porous media. By means of extensive direct numerical simulations of the Darcy-Rayleigh-Taylor model, we demonstrate the existence of a transition from three-dimensional (3D) to 2D phenomenology when the horizontal width of the convective structures becomes larger than the confining scale. At variance with the case of turbulent flows, in which the transition is continuous and a coexistence of the 2D and 3D regimes is observed, the transition in porous media is sharp. We investigate the effects of the transition on the evolution of the mixing process and on the fluctuations of the density field. In the 2D regime, we observe a speedup in the growth rate of the mixing layer with an increase of the inhomogeneities of the density field.