Amplification of long-period waves in shallow coastal embayments of the Great Lakes

Abstract

Lake water level fluctuations provide an important role in flushing shallow coastal embayments in the Great Lakes, especially if the embayment has a resonant response. Specifically, long-period waves (of periods 4–30 min) can excite resonance in coastal embayments, which greatly increases the flushing rates. We describe how resonance can explain the difference in responses of three shallow $$({\text{depth}} \,{\approx }2\, \hbox {m})$$ coastal embayments of Lake Ontario and Lake Huron to similar long-period waves. Higher frequency water level fluctuations were analyzed to determine the most influential frequencies within the embayments. Observations in two adjacent embayments in Lake Huron show dramatic differences between their amplified responses to identical forcing, while in Frenchman’s Bay the oscillations are damped for the whole forcing spectrum. We model the water level response of the shallow coastal embayments to lake long-period wave forcing using a driven Helmholtz harmonic resonator. We compare and find favourable agreement $$(R^{2}=78\,\%)$$ between the amplification of water level fluctuations predicted by our model and field values for nearly enclosed embayments, where the Helmholtz mode dominates the energy of the oscillations. Additionally, strong peaks corresponding to the first three natural modes are observed in the water level oscillations of one of the Lake Huron embayments. This embayment has a wider entrance and its stronger amplified response can be explained using an analytical model based on an asymptotic theory of nonlinear resonance of free long-period oscillations induced by wind waves.