The tidal prism as a dynamic response of a nonlinear harmonic system

As known, the empirical relationship between the equilibrium cross-sectional area of a lagoon inlet and the tidal prism was intuited for the first time by LeConte ["Discussion on the paper, "Notes on the improvement of river and harbor outlets in the United States"by D. A. Watt,"Trans. ASCE 55, 306-308 (1905).] and then formalized by O'Brien ["Estuary tidal prism related to entrance areas,"Civ. Eng. 1(8), 738-739 (1931)]. This relationship requires knowledge of the tidal prism, which can be estimated either using the cubature method or the current data method [Jarrett, Tidal Prism-Inlet Area Relationships (Coastal Engineering Research Center, US Army Corps of Engineers, Fort Belvoir, VA, 1976)], both of which involve the execution of a number of experimental measurements. However, these methods, besides being very expensive, can only provide the prism value in the present condition and do not allow for predictions in the case of significant morphological changes, of both natural and anthropic origin, to the tidal inlet. On the other hand, the hydrodynamic relationship, which links the tidal prism to the product of the tidal range and the basin extension, can only give a coarse estimate of the prism, especially when the value of the tide outside the lagoon is considered. In this work, we propose a simple hydrodynamic relationship based on the dynamic response of a nonlinear harmonic system. This is a relationship that requires the calibration of a single physically based parameter. Through this relationship, knowing the geometric characteristics, the bottom friction of the inlet channel, the surface of the basin, and the tide amplitude in the open sea, it is possible to estimate the tidal prism. The application of this relationship to real cases shows a good agreement with the experimental data.