Amplified exchange rate by tidal forcing of a piecewise-linear Helmholtz bay

Boer, Jordy; Maas, Leo
December 2011
Ocean Dynamics;Dec2011, Vol. 61 Issue 12, p2061
Academic Journal
Sea-level and current measurements have been performed in the Mok Bay, a tidal embayment in the Dutch Wadden Sea, situated on the island of Texel, the Netherlands. Characteristic for this estuary is its nonuniform hypsometry. Oscillations in both water level and inflow of the estuary were observed, with characteristic frequencies of 31 and 48 cycles per day. The significant change in basin shape between low and high water is the cause for the existence of these two frequencies of resonance. Due to its semi-enclosed nature, the basin could at both tidal phases be characterized as a Helmholtz resonator, albeit of different dimensions. Depth measurements were performed to find these characteristic dimensions of the estuary, allowing the determination of its theoretical Helmholtz frequencies. These estimates match to within 10% with the observed frequencies, and this deviation can partly be explained. Although sea level oscillations at these frequencies have small amplitude (of order 1 cm), the accompanying oscillatory flow at the entrance is of similar magnitude as the tidal flow. The water level measurements (spanning only 8 days of data) were therefore modeled using a piecewise-uniform hypsometry that approximates the real hypsometric curve well. The simplified semi-analytical piecewise-linear viscous Helmholtz model captures the observed combination of tidal and eigenoscillations well. However, despite its simplicity, this model is able to display nonlinear behavior for certain parameter values. This is because of the intrinsic nonlinearity that accompanies the matching of the low and high water phases. In the setting studied here, bifurcations up to period 13 were found. This nonlinear type of response may be of importance in facilitating an extra exchange of sediments and nutrients between the Bay and the sea.


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