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UBC Theses and Dissertations

The wave field on a shelf resulting from point source generation, with application to tsunamis King, David Randall


Studies were made to determine the wave field of long surface gravity waves generated on a shelf by a localized source, such as might occur in tsunami generation. Beth analytical and experimental aspects of the problem are investigated. An analytical model is constructed, which examines the field of small amplitude shallow water waves propagating on a shelf of uniform depth. The shelf region is separated from a deep water region of uniform depth by a linear vertical step. The problem is solved on a rotating coordinate system, although the more precise results are obtained for wave frequencies much greater than the inertial frequency for the case of non-rotation. Both exact solutions and asymptotic solutions in the far-field are found for point source excitation. The case of zero-rotation is investigated for both time-harmonic and impulse excitation. The experimental model examines the field of shallow water waves generated under conditions chosen to simulate the analytical model for the case of non-rotation. The resulting field is composed of cylindrical direct and reflected waves and of a plane lateral wave which arises under conditions of total reflection. Have speeds are found which are in agreement with those predicted by ray theory and geometrical optics. Wave amplitudes of the direct and reflected waves behave as cylindrical waves with frictional damping. The lateral wave amplitude decays in accordance with the -1.5 power of the ray optics pathlength of the lateral wave in the deep water, with damping due to friction. Agreement of theory with observation is overall very good. The results are applied to the problem of tsunami generation on a shelf under simple geometrical conditions. Arrival-times of the various field constituents at various points along the shoreline (the inner edge of the shelf) are calculated and the lead time of the lateral wave arrival over the direct wave is determined.

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