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UBC Theses and Dissertations

Resonant interactions between continental shelf waves Hsieh, William Wei


Part I of this thesis develops a theory of nonlinear resonant interactions between continental shelf waves. From the inviscid, unforced long-wave equations for a rotating, homogeneous fluid, it is shown that resonant interactions between three continental shelf waves can occur. Evolution equations governing the amplitude and the energy of individual waves in a resonant triad are derived. The nonlinearity in the governing equations allows energy to be transferred between the waves, but with the total energy conserved. In particular, interactions on an exponential shelf are studied. Part II of this thesis compares the theory from Part I with observations and data from the Oregon shelf. Rotary spectral analysis and cross-shelf modal fitting are the two techniques used for shelf wave detection. Many features characteristic of shelf waves and of the resonant triad interaction theory are found in the current and sea level data. Also, for the first time, shelf waves have been unambiguously identified in both the alongshore and cross-shelf dimensions. The data indicate that the wind generates long continental shelf waves at low frequencies. Nonlinear resonant interactions then transfer energy from the low-frequency long waves to higher frequency shelf waves with much shorter wavelengths. The good agreement between theory and observation suggests that nonlinear energy transfer may play a significant role in shelf wave dynamics.

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