Shallow-Water Flow past Isolated Topography. Part I: Vorticity Production and Wake Formation

Abstract

Abstract The flow of a single layer of shallow water past high three-dimensional topography is studied in a nonrotating environment and in the absence of surface friction. The dimensionless parameters for this problem are the upstream Froude number, the dimensionless mountain height, and a dimensionless measure of the dissipation rate. In part I of this study, high-resolution numerical simulations are utilized to construct a regime diagram for steady left–right symmetric flow and for the domain of parameter space with subcritical upstream conditions. Three distinct regimes occur. They are characterized, respectively, by fore–aft symmetry, essentially inviscid dynamics, and entirely subcritical conditions (regime I); by transition to supercritical flow and the occurrence of a hydraulic jump over the lee slope (regime II); and by the inability of the flow to climb the mountain top resulting in flow separation (regime III). Regimes II and III are associated with a wake that entails significant potential vort...