On tide propagation in convergent estuaries

We revisit the problem of one-dimensional tide propagation in convergent es tuaries considering four limiting cases defined by the relative intensity o f dissipation versus local inertia in the momentum equation and by the role of channel convergence in the mass balance. In weakly dissipative estuarie s, tide propagation is essentially a weakly nonlinear phenomenon where over tides are generated in a cascade process such that higher harmonics have in creasingly smaller amplitudes. Furthermore, nonlinearity gives rise to a se award directed residual current. As channel convergence increases, the dist ortion of the tidal wave is enhanced and both tidal wave speed and wave len ght increase. The solution loses its wavy character when the estuary reache s its "critical convergence"; above such convergence the weakly dissipative limit becomes meaningless. Finally, when channel convergence is strong or moderate, weakly dissipative estuaries turn out to be ebb dominated. In str ongly dissipative estuaries, tide propagation becomes a strongly nonlinear phenomenon that displays peaking and sharp distortion of the current profil e, and that invariably leads to flood dominance. As the role of channel con vergence is increasingly counteracted by the diffusive effect of spatial va riations of the current velocity on how continuity, tidal amplitude experie nces a progressively decreasing amplification while tidal wave speed increa ses. We develop a nonlinear parabolic approximation of the full de Saint Ve nant equations able to describe this behaviour. Finally, strongly convergen t and moderately dissipative estuaries enhance wave peaking as the effect o f local inertia is increased. The full de Saint Venant equations are the ap propriate model to treat this case.