Dynamics of ventilated coherent cold eddies on a sloping bottom

Abstract

eddy is modelled with nonlinear ‘intermediate lengthscale ’ geostrophic dynamics which is coupled to the surrounding fluid. The process of ventilation is modelled with a simple cross-interfacial mass flux parameterization. The surrounding fluid is governed by nonlinear quasi-geostrophic dynamics including eddy-induced vortextube compression. Assuming a relatively weak ventilation rate, a multiple-scale asymptotic theory is constructed to describe the propagation of an initially isolated or coherent baroclinic eddy. Throughout the evolution the eddy is assumed to be interacting strongly with the surrounding fluid. To leading order, the eddy and surrounding fluid satisfy the Stern isolation constraint. The magnitude of the Eulerian velocity field in the surrounding fluid above the eddy is shown to be larger than the swirl velocities in the eddy interior as suggested by experimental data. Also, to leading order, the along-shelf translation speed is given by the Nof formula. The process of ventilation is shown to induce a slowly decaying upslope translation in the propagating eddy, and acts to stimulate a weak slowly decaying topographic Rossby wave field in the surrounding fluid. The important features of the theory are illustrated with a simple example calculation.