Onset of Buoyancy-Driven Convection in Cartesian and Cylindrical Geometries

We perform a linear stability analysis to examine the onset of buoyancy-driven convection relevant to subsurface carbon dioxide sequestration in confined, porous Cartesian and cylindrical domains. We consider Cartesian geometries where the aspect ratio between the two horizontal dimensions is not necessarily equal to one. Two key elements of the stability analysis are the critical time and the critical wavenumber. Lateral boundaries have a much greater effect on the critical wavenumber than on the critical time. The confinement due to these boundaries impedes the onset of convection to the extent that convection cannot even occur in domains that are smaller than a certain size. Large aspect ratios can significantly reduce boundary effects. Patterns of the earliest-growing perturbation mode in the horizontal plane reveal many interesting features. We illustrate several differences between patterns in Cartesian geometries and patterns in cylindrical geometries. Our results may help with understanding the onset of buoyancy-driven convection in real systems where lateral boundary effects are significant.