Removing the separation singularity in a barotropic ocean with bottom friction

Abstract

We consider western boundary outflow in a two-dimensional rectangular basin on a beta plane with bottom drag. The nature of the flow in the boundary layer is determined by a parameter λ which measures the nonlinearity of the flow. When λ is smaller than some critical value λ c, the boundary layer remains attached to the western wall, but as λ is increased above λ c, a separation bubble develops, and the point of separation moves south with increasing λ. If a classical boundary layer expansion as suggested by Prandtl, (Motion of Fluids with Very Little Viscosity, Technical Memo-452, NACA, Washington, DC, 1928) is attempted, a Goldstein separation singularity develops (Quart. J. Mech. Appl. Math. 1 (1948) 43). We show that if an alternative expansion is used inside the boundary layer, this singularity can be removed and the flow can be extended past separation.