On the role of geometry of cross-section in generating flood-dominance in shallow estuaries

Abstract

Shallow estuaries often show tidal asymmetry of flood-dominance in which duration of the flood is shorter and its peak discharge larger than the corresponding values during ebb. Here we propose a simple analytic model for this phenomenon. Noting that in tidal propagation in shallow, narrow estuaries, the dominant terms in the momentum balance are pressure gradient and friction, we preserve only these two terms in the model and linearize the friction. The resulting governing equation for tidal propagation is a diffusion equation with the diffusion coefficient a function of the area and the wetted perimeter of the channel cross-section. The nature of variation of both the area and the perimeter with tidal height depends on the channel geometry, and for most channels the former is more important. Solutions, derived using a perturbation expansion scheme for channels with simple geometries, show that the variation of the diffusion coefficient over a tidal cycle leads to flood-dominance. This and other characteristics of the solution compare favourably with the features seen in observations.