On the influence of an isolated submerged obstacle on a barotropic tidal flow

The influence of an isolated submerged obstacle on the dynamics of a material particle is studied within the limits of a barotropic, quasi-geostrophic model of oceanic S-plane flow, for cases in which the incident how has both steady and tidal components of velocity. Two kinds of motion are shown to occur, namely (i) the particle performs quasi-periodic oscillations in the vicinity of the obstacle or (ii) the particle acquires an infinite character (i.e., the particle leaving the vicinity of the obstacle is irrevocably advected downstream by the background flow). Sufficient conditions are obtained for the existence of both classes of motion. Conditions for domain alternation of the finite and infinite solutions have been derived numerically for different external parameters (e.g., the kinematic characteristics of the flow field and the height of topography). Using the Contour Dynamics Method, results are presented to show how the predicted motions of individual particles can be extended to predict the behaviour of finite water volumes in general and particle admixture patches in particular.