Flows caused by mass forcing in a stratified ocean

Flows due to point sources and sinks of mass are considered on both f- and β-planes. The fluid is assumed to be continuously stratified with constant buoyancy frequency, N, and has no boundaries. Solutions to the flow field giving both horizontal and vertical structure are obtained on large timescales compared with an inertial period for the case when the source/sink flow is started from rest. Steady solutions are obtained through the inclusion of simple Rayleigh damping. On an f-plane the flow is radially symmetric, and a sink (source) generates cyclonic (anticyclonic) swirl due to angular momentum conservation. The nature of the flow of fluid toward the sink depends critically on the ratio f/N. On a β-plane a sink (source) also generates cyclonic (anticyclonic) swirl, but the velocity field is no longer radially symmetric and the circulation about the source/sink drifts westward. Also, the flow of fluid toward the sink intensifies to an eastward flowing jet. The behaviour is described both in terms of vorticity arguments and in terms of the westward propagation of energy by very low frequency Rossby waves. The solution is then used to calculate the surface circulation and vertical density structure in the vicinity of deep ocean convection events where the process is modelled by a simple mass transfer over depth.