Two-inlet lagoon systems: Interaction between basins and effects on tidal prisms

In a lagoon basin, the tidal prism is related to the section of its inlet by a simple monomial relationship (LeConte 1905; O’Brien 1931; Jarrett 1976). Although it is not dimensionally correct and there are sophisticated models in two or three dimensions, this relationship is widely used because of its simplicity. Having a simple relationship can be very important, especially when it is necessary to make quick, albeit approximate, evaluations. To maintain this simplicity, the same monomial relationship is often used in multi-inlet lagoons, even if the initial assumptions are not fully met. Another difficulty in applying a monomial relationship to a multi-inlet lagoon is the definition of the area of each basin. In this paper we propose a simple Eulerian, hydrodynamic, one-dimensional approach based on the dynamic response of a non-linear harmonic system and a harmonic analysis of the interaction between two basins in a lagoon system. With such an approach, the definition of the basin surface is overcome simply by working on topographic control basins. The study leads to the definition of a relatively simple relationship for the estimation of tidal prisms, while maintaining the flexibility of a monomial relationship. If the geometrical characteristics and the bottom friction of the inlet channel, the topographic surface of the basins and the amplitude of the tide in the open sea are known, this relationship can be used to estimate the tidal prism in individual basins.The application of this relationship to two-dimensional numerical cases and real multi-inlet lagoons shows good agreement with experimental data.