Hurst, Rowena Gwendolen Ann; (1991) Boundary and bathymetric effects on the evolution of rotating fluids. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The thesis examines several model flows in an attempt to elucidate the effects of boundaries and/or bathymetry on the development of a rotating flow. In particular, the numerical method of contour dynamics is employed in order to capture the combination of the nonlinear effects of advection and the effects of bottom topography. This method is based on the fundamental property of conservation of potential vorticity. Previous linear work on such topographic effects has not incorporated advection, thus in some cases this conservation law is violated. A brief review of others' work using contour dynamics is presented first, together with some simple examples to illustrate the uses of the method. The first model flow then considered contains a cylindrical underwater obstacle. Various possible flow developments are revealed using the contour dynamics technique and in particular the effects of allowing a free surface are examined. The influence of a sidewall on the formation of Taylor columns is the next problem approached. An underwater semi-cylindrical obstacle, flush against the wall, generates topographic waves in a uniform flow, which travel uni-directionally around the step. In previous such problems, where no wall is present, a Taylor column is set up on the timescale over which the fluid above the obstacle is spun down by Ekman pumping. In this case, however, the presence of the sidewall accelerates the formation of the Taylor column, which is now set up on the shorter topographic timescale. The contour dynamics method is used again in the final chapter. In this problem uniform flow in a channel is forced over a longitudinal step, thus generating topographic waves. The resulting flow is highly dependent on the oncoming flow rate. It is shown that if the flow is sufficiently fast a permanent nonzero relative vorticity region is set up, whilst a slower oncoming flow allows the upstream propagation of the topographic waves, resulting in behaviour similar to that of hydraulic control.

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