Unsteady one‐dimensional flow over a plane: Partial equilibrium and recession hydrographs

Abstract

This paper presents a comparison of solutions of the shallow water (Saint Venant) equations for unsteady one‐dimensional flow over a plane and solutions of the diffusion and kinematic wave equations, which are approximate forms of the Saint Venant equations. In the cases studied, the lateral inflow is constant and positive but may cease before a steady state flow is reached. It is shown that for highly subcritical flow, the criterion proposed by Woolhiser and Liggett is necessary but not sufficient to enable a choice between the shallow water equations and the kinematic approximation. An additional criterion is proposed for these cases.