Morphological equilibrium of short channels dissecting the tidal flats of coastal lagoons

The equilibrium bed profile of tidal channels dissecting the tidal flats of coastal lagoons is studied within a rational one-dimensional framework. A general analytical solution is obtained which expresses the bed profile in terms of a modified longitudinal coordinate, accounting implicitly for channel convergence and adjacent shoals. For values of the relevant parameters typical of costal lagoons, inertia and friction effects as well as overtides are shown to provide minor corrections to the equilibrium bed profile. The overall shape of the profile is also shown to be slightly affected by the equilibrium condition used in its derivation, consisting in a requirement on either residual erosion/deposition fluxes or maximum velocity. In particular, the asymptotic form of the analytical solution is common to both the equilibrium requirements, thus suggesting the existence of general morphological relationships relating the depth at the channel mouth or, alternatively, the length of the channel to the tidal amplitude, to the degree of channel convergence, to the critical velocity for erosion/deposition and to the extent of intertidal storage areas. The profile shape is affected as well; for instance, nearly constant-depth channels tend to form when convergence is strong. The equilibrium configuration also implies that a power law relationship of the type proposed by O'Brien-Jarret-Marchi for tidal inlets, relating the channel cross section to the tidal prism, holds throughout the entire channel. Finally, the theoretical profile is shown to reasonably reproduce the bed configurations observed in a number of tidal channels surveyed within the Lagoon of Venice (Italy).