Tidal wave diffraction by channels and bays

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Abstract
A Kelvin wave in a semi-infinite ocean with a narrow (compared with the wavelength) continental shelf is diffracted by a narrow gap that feeds any of a second semi-infinite ocean, a semi-infinite channel, a closed channel of finite length, a small bay, or a channel terminated by a bay. An equivalent electrical circuit is constructed, in which the incident-wave displacement in the gap appears as the input voltage and the flow into the gap appears as the input current. Approximations to the elements of this circuit are constructed from a quadratic functional that is derived from the integral equation implied by the boundary-value problem. The phase shift in the diffracted Kelvin wave is calculated, and numerical results are given for representative configurations. The general results are applicable to other tidal waves in the semi-infinite ocean, e.g., a Poincaré wave. A model of San Francisco Bay, opening into the ocean through a short, narrow channel (the Golden Gate) and fed by rivers through a long channel (Carquinez Straits), is constructed. It yields a resonant period of 4.6h and a time delay of 3.6 sec for a semi-diurnal (12.4h) Kelvin wave.

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