Linear stability analysis and nonlinear simulations of convective dissolution in an inclined porous layer between impermeable surfaces.

Convective dissolution can occur in porous media when a given solute dissolves in a host layer from above and increases the density of the host solution. Buoyancy-driven fingering can then develop, which increases the transfer flux of the solute. We investigate here numerically the properties of this convective dissolution when the porous host layer is inclined by an angle θ relative to the horizontal direction. We consider an incompressible flow in porous media governed by Darcy's law, driven by density gradients associated with the concentration of the dissolving solute. The model problem focuses on the case of a very long (infinite) tilted porous layer limited by two parallel impermeable surfaces. A linear stability analysis and nonlinear simulations are performed using the Boussinesq approximation. A vorticity-stream function formulation is adopted to solve the two-dimensional hydrodynamic field through the finite element method. We find that the inclination of the interface decreases the growth rate of the instability and the range of unstable wavenumbers, delaying or even suppressing the onset of the fingering instability. Moreover, it introduces a drift velocity on the perturbations, which is characterized here in both the linear stability analysis and the nonlinear simulations.