A LINE SINK IN A ROTATING STRATIFIED FLUID

The two-dimensional flow of an unbounded rotating stratified fluid towards a link sink is studied. The initial-value problem of suddenly initiating the sink flow is solved in Laplace space for a non-diffusive, inviscid fluid using the linearized Boussinesq equations. The solution shows that the sink flow is established by inertio-gravity waves radiated from the sink and that the initial development of the flow depends critically on the ratio of the inertial frequency, f, to the buoyancy frequency, N. For f < N the flow collapses to a horizontal withdrawal layer structure. The final steady state resembles potential flow in which the vertical axis is shrunk by a factor of f/N with a superimposed azimuthal velocity. Viscous, diffusive and nonlinear effects are studied using scaling analysis. A classification scheme based on two parameters delineating various force balance regimes and giving the corresponding withdrawal layer thicknesses is presented. The results show that under certain conditions rotation may cause a thicker withdrawal layer than would be observed if there were no rotation.