The semi-diurnal tide in Hudson Strait: a resonant channel oscillation

An extension of the classical Helmholtz resonator is developed to account for salient aspects of the semi- diurnal tidal resonance observed in the Hudson Bay/Hudson Strait system. The model allows for convergence/divergence of the flow in a channel connecting an inner basin, representing Hudson's Bay, to the open ocean. Accordingly, the model admits two modes of variability. One is the standard Helmholtz mode in which the largest sea level variability occurs within the inner basin. The model also supports a mode in which the greatest sea level variability occurs in the channel, with relatively weak variations in the inner basin. A distinguishing characteristic of this channel mode, the 180º phase difference in the currents at the ends of the channel, is consistent with volume transports from a tidal model of the region. Non-dimensional parameters that govern the response are identified and evaluated based on the physical dimensions of the Hudson Bay/Hudson Strait region. The results suggest that the channel mode is resonant in the strait near semi-diurnal tidal periodicities, in general agreement with observations and more complex models.