On the boundary layer structure of differentially heated cavity flow in a stably stratified porous medium

Abstract

Citation: Daniels, P.G. (2007). On the boundary layer structure of differentially heated cavity flow in a stably stratified porous medium. Journal of Fluid Mechanics, 586, pp. 347-370. doi: 10.1017/S0022112007007100 This is the unspecified version of the paper.This version of the publication may differ from the final published version. This paper considers two-dimensional flow generated in a stably stratified porous medium by monotonic differential heating of the upper surface. For a rectangular cavity with thermally insulated sides and a constant-temperature base, the flow near the upper surface in the high-Darcy-Rayleigh-number limit is shown to consist of a double horizontal boundary layer structure with descending motion confined to the vicinity of the colder sidewall. Here there is a vertical boundary layer structure that terminates at a finite depth on the scale of the outer horizontal layer. Below the horizontal boundary layers the motion consists of a series of weak, uniformly stratified counter-rotating convection cells. Asymptotic results are compared with numerical solutions for the cavity flow at finite values of the Darcy-Rayleigh number. Permanent