Rayleigh-Darcy convection with hydrodynamic dispersion

We investigate the effect of hydrodynamic dispersion on convection in porous media by performing direct numerical simulations (DNS) in a two-dimensional Rayleigh-Darcy domain. Scaling analysis of the governing equations shows that the dynamics of this system are not only controlled by the classical Rayleigh-Darcy number based on molecular diffusion, Ra-m, and the domain aspect ratio, but also controlled by two other dimensionless parameters: the dispersive Rayleigh number Ra-d = H/alpha(t) and the dispersivity ratio r = alpha(l)/alpha(t), where H is the domain height and alpha(t )and alpha(l) are the transverse and longitudinal dispersivities, respectively. For Delta = Ra-d/Ra-m > O(1), the influence from the mechanical dispersion is minor; for Delta less than or similar to 0.02, however, the flow pattern is determined by Ra-d while the convective flux is F similar to c(Ra-d)Ra-m for large Ra-m. Our DNS results also show that the increase of mechanical dispersion, i.e., decreasing Ra-d, will coarsen the convective pattern by increasing the plume spacing. Moreover, the inherent anisotropy of mechanical dispersion breaks the columnar structure of the megaplumes at large Ra-m, if Ra-d < 5000. This results in a fan-flow geometry that reduces the convective flux.