Tidal flow field in a small basin

Abstract

The tidal flow field in a basin of small dimensions with respect to the tidal wavelength is calculated. Under these conditions, the tide becomes a standing wave oscillating synchronously (with a flat water surface) over the whole basin. The shallow water equations can thus be strongly simplified, expressing the discharge vector field in terms of a potential function and a stream function. The potential function can be independently solved with the continuity equation, and is responsible for the total water balance in the basin. Moreover, the flow field derived from the potential function is shown to represent the tidal motion in a deep basin with flat bottom. Departures from this situation are treated with a stream function, that is, a correction for the potential function solution, and is solved through the vorticity equation. The stream function accounts for the nonlinear inertial terms and the friction in the shallow water equations, as well as bottom topography. In basins where channels incise within shallow tidal flats, the solution demonstrates that friction redistributes momentum, increasing the flow in the channels and decreasing it on the flats. The model is tested in San Diego Bay, California, with satisfactory results.