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.