Tidal inlets and estuaries: Comparison of Bruun, Escoffier, O'Brien and attractors
The authors have shown previously that over very long time scales a barrier estuary or tidal inlet will tend towards one of two states, called attractors. In this paper it is shown how that analysis represents an extension and generalisation of three earlier procedures. There are three widely recognised quantitative semi-empirical procedures describing the long term equilibrium dimensions of the entrance channel of barrier estuaries and tidal inlets. The best known of these laws is the tidal prism-entrance area relation, often referred to as the O'Brien equation. The second procedure is based on the Escoffier or closure diagram, comprising a simple hydrodynamic relationship between the entrance area and the entrance velocity together with an empirical "equilibrium velocity". The third is the set of rules developed by Bruun that relate the entrance channel stability to the longshore sediment supply and the entrance channel sediment transport capacity. Each of these is based on major simplifications that restrict its utility and range of validity more than is usually recognised. The attractor analysis, while still based on a lumped model, adds sediment transport and deposition/scour equations and enables the use of more realistic entrance hydrodynamics. It predicts the rates of change and presents the results on a practical "attractor map". The predictions of the three empirical laws are compared with the attractor map and their practical application is critically compared. The empirical laws are shown to provide broadly equivalent predictions to the attractor map, but over limited ranges of estuary conditions. In particular, none of the empirical laws identifies the entrance closure state or describes conditions near closure.