Title:

Analytic techniques for shortterm ocean current forecasting

This thesis concerns the motion of oceanic vortices and comprises two parts. Part I examines the dynamics of point vortices in a twolayer fluid near large amplitude, sharply varying topography, e.g. continental shelf regions. Topography takes the form of an infinitely long step change in depth and the twolayer stratification is chosen such that the height of topography in the upper layer is a small fraction of the overall depth, enabling quasigeostrophic theory to be used in both layers even though the topography is large amplitude. An analytic expression for the dispersion relation of free topographic waves in this system is found. Weak lowerlayer vortices are studied using linear theory and, depending on their sign, are able to produce significant topographic wave radiation in their wakes. Upperlayer vortices produce relatively small amplitude topographic wave radiation. Contour dynamics results are used to investigate the nonlinear regions of parameter space. For lowerlayer vortices linear theory is a good approximation, but for upperlayer vortices complicated features evolve and linear theory is only valid for weak vortices. The motion of hetons (two vortices, one in each layer) and dipoles are also studied. Part II involves the investigation and prediction of the motion of Loop Current Eddies (LCE's) in the Gulf of Mexico. By incorporating the major features of LCE's into a simple eddy model it is attempted to discover if it is possible to deduce the characteristics of a distant eddy from a set of measured velocities at a fixed location and further, predict the subsequent motion of the eddy. First, a circular model for the eddy shape is adopted and the Helmholtz equation is solved in the farfield. Second, a more sophisticated, precessing, elliptical model is developed, the solution involving Mathieu functions. In both cases comparison with actual current meter data is used to demonstrate the validity of the models.
