Mathematical model of tidal water transport by a partial blockage of a coastal lagoon

In this paper, an analysis is done on the tidally forced dynamical behavior of a partially blocked coastal lagoon. A non-linear differential equation has been deduced for the evolution of the water depth in the blocked part of the lagoon as a function of the tidally driven water depth in the ocean connected part. This dynamical problem depends on two non-dimensional parameters: the relative amplitude of tidal wave and the non-dimensional tidal period (related to the filling time of the blocked part). For very small values of the relative amplitude of the tidal wave, the problem depends only on one parameter. The evolution equation is numerically solved for a wide range in the parametric space, obtaining the relative amplitude of the water depth oscillations in the blocked part, its phase lag and the mean water depth behind the bridges. The specific case of the Chelem lagoon has been studied, which has been divided by a road with only two small bridges. Water flows from the open ocean-connected part of the lagoon to the enclosed part only through the bridges. The analysis shows the response if a new bridge is built or one of the actual bridges is removed.