# Onset of convective instability in an inclined porous medium

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## 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 ($\theta$) until it reaches a cut-off angle beyond which the system remains stable. The cut-off angle increases with the Rayleigh number, $Ra$. The evolving wavenumber at the onset exhibits a lateral velocity that depends non-monotonically on $\theta$ and linearly on $Ra$. Instabilities are observed in gravitationally stable configurations ($\theta \geq 90^{\circ}$) solely due to the non-uniform 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 CO$_2$ sequestration.
Original language English 014104 (In-press) 8 Physics of Fluids 34 1 5 Jan 2022 https://doi.org/10.1063/5.0073501 E-pub ahead of print - 5 Jan 2022

### Bibliographical note

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Luther, EE, Dallaston, MC, Shariatipour, SM & Holtzman, R 2022, 'Onset of convective instability in an inclined porous medium', Physics of Fluids, vol. 34, no. 1, 014104, pp. (In-press) and may be found at https://dx.doi.org/10.1063/5.0073501

## Keywords

• physics.flu-dyn

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