A Simple Theory for the Fate of Buoyant Coastal Discharges*

Abstract

Abstract A simple theory that predicts the vertical structure and offshore spreading of a localized buoyant inflow onto a continental shelf is formulated. The theory is based on two competing mechanisms that move the buoyant fluid offshore: 1) the radial spread of the lighter water over the ambient water, being deflected by the Coriolis force and producing an anticyclonic cyclostrophic plume, and 2) offshore transport of buoyant water in the frictional bottom boundary layer that moves the entire plume offshore while maintaining contact with the bottom. The surface expression of the cyclostrophic plume moves offshore a distance ys = 2(3g′h0 + υ 2i)/(2g′h0 + υ 2i)1/2f,where g′ is reduced gravity based on the inflow density anomaly, h0 is the inflow depth, υi is the inflow velocity, and f is the Coriolis parameter. The plume remains attached to the bottom to a depth given by hb = (2Lυih0f/g′)1/2,where L is the inflow width. Both scales are based solely on parameters of the buoyant inflow at its source. There...