Resonant modulation of the flow in a tidal channel

Abstract

The coupling between a quarter‐wave resonance in a coastal bay and a Helmholtz mode in an adjacent cove (connected to the bay through a narrow channel) is investigated by comparing field measurements to analytical and numerical model predictions. Pressure and velocity spectra from locations throughout the bay reveal an oscillation with a period of approximately 1 hour, consistent with a quarter‐wave seiche mode. The associated sea surface displacements throughout the bay are small (less than 5 cm RMS, i.e., only 10% of the tidal elevation). Velocities within the channel are significantly modulated in the 1‐hour band, with amplitudes up to 40% of the peak tidal current. The analytical model shows that the modulation of the channel flow results from the interaction between the quarter‐wave mode in the main basin and a Helmholtz resonance in the cove, also with a period near 1 hour. The amplitude and phase of the 1‐hour oscillation varies through the tidal cycle because of the change in Helmholtz frequency with tidal elevation. Good quantitative agreement between the data and the model predictions is obtained if a drag coefficient approximately 3–4 times larger than the classical value of 3 × 10−3 is used in the channel and cove.