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.

The well-known empirical relationship between the equilibrium cross-sectional area of tidal inlet entrances (A) and the tidal prism (P), first developed by O'Brien (1931), has been extensively reviewed. Our theoretical investigations indicate that a unique A-P relationship should only be expected for clusters of inlets that are phenomenological similar (i.e. fairly similar hydrodynamic and morphological conditions), and that the exponent q in the A-P relation should be larger than 1. However, relevant published data available to date do not clearly support this theoretical finding. A re-analysis of the available data sets by Stive et al. (2009) indicated that they may not be sufficiently reliable to verify our theoretical finding with regard to q>1 due to the violation of the condition of phenomenological similarity, and possibly also due to violating the initial definitions given by O'Brien (1931) in estimating the tidal prism. The resolution of this issue is important because slightly different values of q result in significantly variable values for the equilibrium cross-sectional area of the tidal entrance. This may have significant implications in determining the true stable equilibrium entrance cross-sectional area. Here we present a re-analysis of the available data with a focus on determining the phenomenological dependencies of the A-P relationship. The available A-P data from the US Pacific, Atlantic and Gulf coasts (Jarrett, 1976 and Powell, 2003) have been re-scrutinized and categorized following the above mentioned phenomenological similarity criteria, viz. similar tidal range, similar sediment size, similar littoral transport and similar hydraulic radius. All together, some 20 different categories were considered and A-P relationships were obtained for each category. Generally, high correlations were found between the stable inlet predicted by each A-P relationship and the corresponding data. However, only in a limited number of categories were they significantly better than the correlations for the complete datasets. Finally, we point out that only in a number of categories the q value associated with the A-P relationship exceeded unity as suggested by the theoretical derivations. In the majority of categories the q value associated with the A-P relationship does not exceed unity. This is truly disappointing, and we have no physical explanation for this and consider this issue unresolved.