Attractors for the Entrance State of a Tidal Estuary in the Presence of a Multi-Harmonic Tide
The tidal dynamics of a barrier estuary have frequently been modelled as a tidal basin linked to the ocean by a narrow entrance channel and forced by a sinusoidal ocean tide. In this approach the calculated velocities in the entrance channel are used to infer scouring if the entrance area is smaller than an "equilibrium" value and deposition if it is larger. The equilibrium entrance dimensions and velocity define an attractor in the terminology of system dynamics. In a previous paper the authors have followed this model with the addition of a sediment transport function. Their results predicted the existence of two attractors; the attractor may be a single set of values of the system variables or a repeated cycle of values. The present study has improved the realism of this model by using a multi-harmonic ocean tide. The same attractors were found but the range of conditions under which they occurred was changed, in general resulting in a deeper entrance channel than in the case of a sinusoidal tide. These results define the possible regimes of a given estuary, and can be used to assist in decision making regarding the management of an estuary.