Application of Riemann-Green Functions on Solving Linearized Saint-Venants Equations

This study aims to address the variations of the open-channel flows that are originally kept in a uniform steady state and then slightly perturbed by injecting a periodic lateral inflow. Uses of some transformations and of the Riemann-Green function method would yield a simple discharge solution in an integral form. The results show that hydrographs of both the main flow discharge and the lateral inflow oscillate with the same period but out phase after a time interval. In addition, flows transported in channels with gentler bottom slopes have longer transient times. The shortcoming in using the integral solution suggested in the present investigation is that the Froude numbers of the unperturbed flows must be >1.5.