Periodic Wind-Driven Circulation in an Elongated and Rotating Basin

An idealized model is developed for the three-dimensional response of a coastal basin (e.g., lagoon, bay, or estuary) to time-periodic wind stress. This model handles basins that are deeper and/or shallower than an Ekman depth with wind forcing frequencies ranging from subinertial to superinertial. Here the model is used to describe how the response (current and sea level) of a basin deeper than one Ekman depth depends on the wind forcing frequency. At low subinertial frequencies, the response is similar to the steady wind case and is hence called “quasi steady.” There is a near-surface Ekman transport to the right of the wind balanced by a return flow at depth. Lateral bathymetric variations introduce an along-basin circulation that decays with increasing frequency and sets the extent of the quasi-steady response in the frequency domain. At the inertial frequency, the wind forces a damped resonant response with large vertical shear and weak depth-integrated flow. This result is potentially important for coastal basins located near ±30° latitude and forced by a diurnal breeze. At superinertial frequencies, the response becomes irrotational and is amplified near seiche frequencies. The response to a sudden onset of wind is computed in the time domain and confirms that the slow growth of the along-basin circulation controls the spinup process. The response of basins shallower than an Ekman depth, and the validity of the model inside semienclosed basins, are also discussed.