The effect of a topographic high on the morphological stability of a two-inlet bay system

The cross-sectional stability of two tidal inlets connecting the same back-barrier lagoon to the ocean is investigated. The condition for equilibrium is the cross-sectional area tidal prism relationship. In an earlier study [Van de Kreeke, J., 1990. Can multiple inlets be stable? Estuarine, Coastal and Shelf Science 30: 261–273.], using the same equilibrium condition, it was concluded that where two inlets connect the same basin to the ocean ultimately one inlet will close. One of the major assumptions in that study was that the water level in the basin fluctuated uniformly. In hindsight this assumption might be too restrictive. For example, in the Wadden Sea the back barrier lagoon consists of a series of basins, rather than one single basin, separated by topographic highs. These topographic highs limit but do not exclude the exchange of water between the sub-basins. For this reason in the present study, a topographic high in the form of a weir was added, separating the back-barrier lagoon in two sub-basins. The water level in the sub-basins, rather than in the back-barrier as a whole, is assumed to fluctuate uniformly. For this schematization the hydrodynamic equations are solved using a finite difference method. The results, together with the equilibrium condition, yield the equilibrium flow curve for each of the inlets. The intersections of the two equilibrium flow curves represent combinations of cross-sectional areas for which both inlets are in equilibrium. The stability of the equilibriums was investigated using a non-linear stability analysis resulting in a flow diagram. Calculations were carried out for different inlet and weir characteristics. Sinussoidal tides were the same for both inlets. The results show that for relatively large wetted cross-sectional areas over the topographic high, approaching the situation of a single basin, there are no combinations of inlet cross-sectional areas for which both inlets are in a stable equilibrium. This supports the conclusion in the earlier study. For relatively small wetted cross-sectional areas over the topographic high there is one set of stable equilibriums. In that case the two-inlet bay system approaches that of two single-inlet bay systems.