Simple Models of Flow over Deep Ocean Sills: Planetary and Semigeostrophic Solutions

Abstract

Simple inverted reduced-gravity models of flow over deep ocean sills are considered, with emphasis placed on the case for which sills are wide with respect to the abyssal Rossby radius. When the length scale of the flow is also large compared to the Rossby radius, an f-plane version of the planetary geostrophic (PG) equations applies. These equations, however, predict a collapse in scale of the flow so that the PG approximation breaks down and higher-order dynamics must be evoked. Whether or not the collapsing PG dynamics give way to semigeostrophy (SG) or to some other balance regime is also discussed. Next, the steady semigeostrophic equations typically used in rotating hydraulics studies are considered. For relatively wide sills, as well as for narrow sills that are not elongated, the path taken by the overflow is not well constrained by the sill geometry alone. The collapsing PG problem, however, suggests that the appropriate axis of flow follows a branch of the seperatrix isobath. Also suggested by the PG dynamics is that there may be a mass of quiescent water adjacent to the overflow current. Dependence of the maximum flux across the sill on assumptions regarding the flow path and the presence or absence of a quiescent water mass are therefore considered. These are compared with dependencies on sill width and the potential vorticity of the overflow. Finally, flow upstream and downstream of the sill is considered. In particular, a case in which multiple equilibria exist downstream of the sill is discussed.