A Simple Theory for the Fate of Buoyant Coastal Discharges

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 + ??2i)/(2g?h0 + ??2i)1/2f,where g? is reduced gravity based on the inflow density anomaly, h0 is the inflow depth, ?i is the inflow velocity, and f is the Coriolis parameter. The plume remains attached to the bottom to a depth given by hb = (2L?ih0f/g?)1/2,where L is the inflow width. Both scales are based solely on parameters of the buoyant inflow at its source. There are three possible scenarios. 1) If the predicted hb is shallower than the inflow depth, then the bottom boundary layer does not transport buoyancy offshore, and a purely surface-advected plume forms, which extends offshore a minimum of more than four Rossby radii. 2) If the hb isobath is farther offshore than ys, then transport in the bottom boundary layer dominates and a purely bottom-advected plume forms, which is trapped along the hb isobath. 3) If the hb isobath is deeper than the inflow depth but shoreward of ys, then an intermediate plume forms in which the plume detaches from the bottom at hb and spreads offshore at the surface to ys. The theory is tested using a primitive equation numerical model. All three plume types are reproduced with scales that agree well with the theory. The theory is compared to a number of observational examples. In all cases, the prediction of plume type is correct, and the length scales are consistent with the theory.