The effect of tidal exchange on residence time in a coastal embayment

Numerical simulations of an idealized lagoon that is connected to the ocean via a tidal inlet show that the mean residence time is inversely proportional to tidal exchange. In the Delft3D model the tidal exchange is controlled by varying the inlet length, width and depth. These changes in the inlet geometry affect the tidal prism and the ebb/flood flow structure, which are shown to control the exchange of lagoon water with seawater. To map residence time within the lagoon, a new method that implements dye tracer is developed and shows that the tidally averaged residence time exhibits significant spatial variability. For inlet systems in which, as a first approximation, the lagoon can be described by a uniformly fluctuating water level, a simple transport model is developed to elucidate the specific processes that control tidal exchange and their effect on residence time. In this transport model tidal exchange is decomposed into two fractions, an ocean exchange fraction and a lagoon exchange fraction. It is shown that both fractions need to be included to better describe tidal exchange. Specifically, inclusion of a lagoon exchange fraction improves previous tidal prism models that assume complete mixing in the lagoon. The assumption of complete mixing results in an under-prediction of residence time. Relating the spatially averaged residence time results to the exchange fractions for each inlet geometry show that the residence time is inversely proportional to the product of the tidal exchange fractions. For these single inlet systems, Keulegan's 0-D hydrodynamic model shows good agreement with Delft3D in predicting the tidal prism, maximum flow velocity, and exchange fractions. With these parameters, estimates of the mean residence time can be reached through a relationship derived from the simple transport model.