Onset of convective instability in an inclined porous medium

The diffusion of a solute from concentrated source into horizontal, stationary, fluid-saturated porous medium can lead to convective motion when gravitationally unstable density stratification evolves. In an inclined medium, the flow becomes intricate as it originates combination and lateral flow, which is dominant near solute. Here, we investigate role inclination on onset instability by linear stability analyses Darcy's law mass conservation for concentration field. We find that time increases with angle ($\theta$) until reaches cut-off beyond system remains stable. Rayleigh number, $Ra$. evolving wavenumber at exhibits velocity depends non-monotonically $\theta$ linearly Instabilities are observed in stable configurations ($\theta \geq 90^{\circ}$) solely due non-uniform base generating shear commonly associated Kelvin-Helmholtz instability. These results quantify tilt instabilities, great importance geological CO$_2$ sequestration.