Effects of surface thermal forcing on stratified flow past an isolated obstacle.

摘要

The present study investigates basic aspects of the flow of a density-stratified fluid past three-dimensional obstacles for Froude number {dollar}sim{dollar} O(1) and isolated surface thermal forcing representative of diurnally varying mesoscale flows past mountainous islands such as Hawaii. In order to minimize parameter space, we have excluded the effects of friction, rotation, nonuniform ambient flow, and the complexities of realistic surface boundary layer and terrain. Through simple scaling arguments, we deduce that the parameter {dollar}etasp*{dollar} {dollar}{dollar}lbracketasp*equiv{lcub}Lsp*bar Qover Uh{rcub}left({lcub}partialbarthetaoverpartial z{rcub}right)sp{lcub}-1{rcub} sim{lcub}cal O{rcub}(1) rm for mesoscale flowsrbrack{dollar}{dollar}controls thermally forced flows for a given Froude number, and we provide crude estimates of a flow response for a range of {dollar}etasp*{dollar}. The principal question addressed is for what values of {dollar}etasp*{dollar} will a transition occur from the low-Froude-number flow regime, characterized by the stagnation and splitting of the lower upwind flow, to the regime in which flow passes over rather than around the obstacle. We show that the linear theory captures such a tendency consistently with simple scaling arguments. To provide quantitative measures of flow variability with the Froude number and {dollar}etasp*{dollar}, we employ an efficient isentropic numerical code and summarize the results of numerous simulations in the form of a regime diagram. The principal result is a simple criterion for the transition of a heated flow from the blocked to unblocked flow regime. We illustrate the relevance of the idealized study to natural flows with an example of applications to a flow past the Hawaiian Archipelago.