Flow past a Cylinder on aβPlane, with Application to Gulf Stream Separation and the Antarctic Circumpolar Current

Abstract

The classical problem of flow past a cylinder is revisited in the context of understanding two oceanographic phenomena: separation of the Gulf Stream from the North American coastline at Cape Hatteras and the interaction of the Antarctic Circumpolar Current with topographic obstacles. Numerical solutions are presented for eastward, barotropic flow past a cylinder in a β-plane channel. The solutions are dependent on two nondimensional parameters: the Reynolds number, Re, and a nondimensional β parameter, β̂. In line with previous studies, increasing β̂ reduces the separation downstream of the cylinder but introduces a blocked stagnant region upstream of the cylinder, flanked by two inertial jets. The large β̂ limit is relevant to the interaction of the Antarctic Circumpolar Current with topographic obstacles such as the Kerguelen Plateau. However, a new regime is obtained for high Reynolds number (Re > 200) and moderate β parameter (β̂ ∼ 10–100) with two separated jets downstream of the cylinder. These jets can extend a considerable distance, maintained by breaking Rossby waves in the turbulent wake of the cylinder, within which there is a downscale cascade of vorticity and an upscale cascade of energy toward the Rhines scale. Through a series of numerical experiments, the authors demonstrate the relevance of this regime to the separation of a boundary current from a cape. The implications are that Gulf Stream separation at Cape Hatteras is the consequence of both the high Reynolds number in the ocean and the moderate β parameter associated with the curvature of the coastline at Cape Hatteras. Results also suggest that geostrophic eddy fluxes are essential in maintaining a tight separated jet.