Non-linear channel–shoal dynamics in long tidal embayments

Abstract

The dynamics of finite-amplitude bed forms in a tidal channel is studied with the use of an idealized morphodynamic model. The latter is based on depth-averaged equations for the tidal flow over a sandy bottom. The model considers phenomena on spatial scales of the order of the tidal excursion length. Transport of sediment mainly takes place as suspended load. The reference state of this model is characterized by a spatially uniform M₂ tidal current over a fixed horizontal bed. The temporal evolution of deviations from this reference state is governed by amplitude equations: these are a set of non-linear equations that describe the temporal evolution of bed forms. These equations are used to obtain new morphodynamic equilibria which may be either static or time-periodic. Several of these bottom profiles show strong similarity with the tidal bars that are observed in natural estuaries. The dependence of the equilibrium solutions on the value of bottom friction and channel width is investigated systematically. For narrow channels (width small compared to the tidal excursion length) stable static equilibria exist if bottom friction is slightly larger than r_cr. For channel widths more comparable to the tidal excursion length, multiple stable steady states may exist for bottom friction parameter values below r_cr. Regardless of channel width, stable time-periodic equilibria seem to emerge as the bottom friction is increased.