Onset of convective instability in an inclined porous medium

Abstract

The diffusion of a solute from a concentrated source into a horizontal, stationary, fluid-saturated porous medium can lead to a convective motion when a gravitationally unstable density stratification evolves. In an inclined porous medium, the convective flow becomes intricate as it originates from a combination of diffusion and lateral flow, which is dominant near the source of the solute. Here, we investigate the role of inclination on the onset of convective instability by linear stability analyses of Darcy's law and mass conservation for the flow and the concentration field. We find that the onset time increases with the angle of inclination (θ) until it reaches a cutoff angle beyond which the system remains stable. The cutoff angle increases with the Rayleigh number, Ra. The evolving wavenumber at the onset exhibits a lateral velocity that depends non-monotonically on θ and linearly on Ra. Instabilities are observed in gravitationally stable configurations (θ≥90°) solely due to the nonuniform base flow generating a velocity shear commonly associated with Kelvin–Helmholtz instability. These results quantify the role of medium tilt on convective instabilities, which is of great importance to geological CO2 sequestration.