Convective instability in layered sloping warm-water aquifers

摘要

In a recent paper (McKibbin et al., 2011) some questions were posed about fluid and heat flows in a stratified groundwater aquifer with a small slope, subject to a perpendicular temperature gradient. The strength of shear flows in the direction of the maximum slope and the associated convected heat flux were quantified. This paper provides a method to quantify the stability of such flows and the shape and amplitude of convective rolls that may form when the critical Rayleigh number is exceeded. The associated issue of how the mean flow-path of a soluble species introduced into the aquifer is affected by the convective rolls, is also considered. The models formulated are for buoyancy-driven fluid flow in long, sloping warm-water aquifers with both smoothly- and discretely-layered structures.