The Ekman Vertical Velocity in an Enclosed Beta-Plane Ocean

by W. Lawrence Gates

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An inital effort to develop a theory of upwelling in bounded oceanic basins in a manner analogous to that used in the theory of steady wind-driven currents. The vertical flux beneath the surface boundary layer is determined by balancing the stress induced in this layer by the prescribed wind stress and surface temperature with the divergence of an assumed geostrophic interior flow. The equilibrium surface height over an enclosed basin is thus formulated as a boundary-value problem whose solution leads directly to the Ekman vertical velocity. The corresponding vertical velocity at the top of the boundary layer over a level bottom is also determined. Under idealized conditions, the solutions for Ekman vertical velocity appear to be reasonable approximations to oceanic upwelling, particularly when the surface thermal forcing is considered. Previously, the application of the Ekman theory on an oceanic scale has been limited by neglect of the latitude variation of the Coriolis parameter, or beta-effect, and by formulation as a local rather than a boundary-value problem.

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