Analytical solution of channel flow model with downstream control

Abstract

The effect of the downstream boundary condition on the flow in a channel reach is explored through the analysis of the linearized St Venant equations. It is found that there are two effects of the inclusion of the downstream boundary condition: the direct upstream transmission of the downstream boundary condition and the generalization of the upstream response from a single term to an infinite series. The relative effects of upstream and downstream conditions on the water level at any intermediate point in the reach are evaluated.