Unsteady Abyssal Circulation Driven by a Discrete Buoyancy Source in a Continuously Stratified Ocean

Abstract

Analytical and numerical models are presented for linear quasigeostrophic buoyancy-driven flow forced bya time periodic pulsating point mass source in a continuously stratified, incompressible ?-plane ocean withconstant Brunt?Väisälä frequency. The source represents the seasonal introduction of dense water into the abyssalocean and is located on a linear sloping bottom of arbitrary orientation. The ocean domain is horizontallyunbounded and of infinite depth. Rayleigh friction is incorporated into the horizontal momentum equations andappears at order Rossby number in the quasigeostrophic expansions. In the density equation the influence ofRayleigh friction and Laplacian friction are each considered in turn. Analytical solutions are obtained in the case of 1) a midlatitude ? plane with no bottom slope and 2) an fplane with a bottom slope. In both of these problems the fluid is initially at rest and the mass source is switchedon and maintained. A three-dimensional radiating field of baroclinic Rossby waves is generated, which arebottom trapped in the second problem. If the time between successive mass pulses is sufficiently long to enablethe free waves to dominate the solution, it is found that the azimuthal wavelength of the bottom-trapped vorticitywave decreases thereby producing a series of elongated vortices. The present generation of ocean generalcirculation models would be unable to resolve this bottom-trapped flow. Numerical solutions are presented for the case of a sloping bottom of arbitrary orientation on a ? plane whenthe time periodic source exists for all time. During each cycle of the forcing a bottom-trapped anticyclonicvortex is generated at the source and propagates in a direction dictated by the relative role of the planetary andtopographic beta effects. The horizontal distance that the vortex propagates before decaying is larger whenLaplacian mixing is incorporated in the density equation rather than Rayleigh damping. A study of how slopemagnitude and orientation influences the solution is presented.