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

Abstract

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 β-plane ocean withconstant Brunt–Vaisala 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 β 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 Rossb...