Ocean Circulation with Localized Vorticity Forcing
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Two types of circulations are found in the deep ocean: recirculating cells and basin-wide gyres. This thesis examines the physics of such circulations in several contexts. Consideration is given first to a steady, linear, barotropic fluid in a semi-infinite domain bounded by a vertical sidewall whose orientation varies from east-west to north-south. The fluid is forced by a point-source of vorticity and dissipation is parameterized as both Rayleigh drag and Laplacian viscosity. The equivalent westward extent of the circulation, accounting for variations in topography, is found to be a strong function of the angle of the solid boundary. When the boundary obstructs the circulation, it decays exponentially with a well defined characteristic decay scale. This decay scale as a function of the angle is found analytically and numerically. A general circulation model is then used to find the time evolution of a weakly baroclinic fluid in a closed domain with sloping sidewalls. The fluid is forced by a small region of wind stress curl, and models with both 2 and 8 vertical layers are used. The initial response is a narrow, recirculating cell that resembles the steady, linear solution in a semi-infinite domain. The circulation evolves, however, into a gyre that encircles the domain. The timing of this evolution depends on the Rossby number, with higher Rossby numbers producing faster evolution. Over a wide range of parameters, no 8-layer model reached a steady state as a recirculating cell. Some 2-layer models with very high gradients in planetary vorticity appeared to reach a quasi-steady state. The decay scales from the semi-infinite domain demonstrate that the western boundary is not long enough to extract significant vorticity from the flow and therefore the recirculating cell is not a steady solution. They also suggest that the Labrador Sea cannot sustain steady, linear, barotropic recirculations. The circulation of a steady barotropic fluid in a periodic channel is considered next. A numerical continuation algorithm is developed to start from a unique linear solution and find successively more nonlinear solutions. The results show that the circulation expands to fill the entire channel as nonlinearity increases, but never splits into a boundary current as was observed in the general circulation model. Finally, the circulation of a steady barotropic fluid in a closed domain with varying bathymetry is considered. The results indicate that both recirculating cells and basin-wide gyres are possible, and that the distribution of f/h lines (where f is the Coriolis parameter and h is the depth of the fluid) is at least as important in determining the steady state as nonlinearity.