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, ${\text{Ra}}_m$, and the domain aspect ratio, but also controlled by two other dimensionless parameters: the dispersive Rayleigh number ${\text{Ra}}_d=H/{\alpha }_t$ 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 $\mathrm{\Delta }={\text{Ra}}_d/{\text{Ra}}_m>O\left(1\right)$, the influence from the mechanical dispersion is minor; for $\mathrm{\Delta }\lesssim 0.02$, however, the flow pattern is determined by ${\text{Ra}}_d$ while the convective flux is $F\sim c\left({\text{Ra}}_d\right){\text{Ra}}_m$ for large ${\text{Ra}}_m$. Our DNS results also show that the increase of mechanical dispersion, i.e., decreasing ${\text{Ra}}_d$, 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 ${\text{Ra}}_m$, if ${\text{Ra}}_d<5000$. This results in a fan-flow geometry that reduces the convective flux.

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• Convection
• Flow instability
• Flows in porous media
• Rayleigh-Taylor instability