Impact of a concentrated lateral inflow and stage–discharge relation imposed at the downstream end of a finite channel for the diffusive wave model

An analytical solution for the diffusive wave model with a concentrated lateral inflow for a finite channel is presented. Flow depth and flow discharge are taken as the upstream boundary, whereas the downstream end is subjected to a stage–discharge relationship. The focus is on analyzing the impact of the lateral inflow concentrated at different locations on the flow discharge and flow depth. Unit-step responses for all the impulse responses for the lateral inflow are also presented and compared with the corresponding results of a semi-infinite channel where the downstream boundary is ignored. For higher Peclet numbers, the semi-infinite channel responses are found to be a satisfactory substitute for the finite channel responses to predict flow discharge, when a flow discharge is imposed at the upstream boundary, and a steady uniform condition is applied at the downstream boundary. However, for lower values of Peclet number, the same is not replicated. Furthermore, for the flow depth responses, the semi-infinite channel results are not appropriate approximations for finite length channel responses since the flow depth is observed to be sensitive to the backwater effect induced by the downstream boundary.