Semi-analytic model of tidal-induced inlet flow and morphological evolution

A semi-analytic model is developed to describe the flow through an inlet between a lagoon and the sea due to a simple tide and the related morphological response of the inlet. The governing equation for the water level variation in the lagoon is derived from the continuity and momentum equations and then solved for quasi-steady conditions yielding analytic expression for the main flow-related properties such as lagoon amplitude, maximum and mean inlet velocity, tidal prism, and retention time. These quantities are expressed in non-dimensional form, where the repletion coefficient is the main independent variable. A sediment balance model is formulated for the inlet that relates changes in the inlet cross-sectional area to the difference between the longshore sediment transport and the transport through the inlet because of the tidal motion. This balance equation can be solved to yield the conditions at equilibrium as well as the evolution towards equilibrium or closure. The semi-analytic model is employed in the balance equation allowing for a close coupling between inlet hydraulics and morphology. Investigation of inlet equilibrium revealed, similarly to the Escoffier curve, two equilibrium situations, one corresponding to stable conditions and one to unstable conditions. The leading parameters in the stability analysis are the repletion coefficient and the longshore transport rate normalized with a fictive inlet transport rate.