Linear Hyperbolic Model for Alluvial Channels

Abstract

The exact linear solutions for the sediment transport and bed form evolution for one‐dimensional sediment‐water two‐phase motion have been obtained using the St. Venant shallow‐water equations with the assumption of quasisteady flow. These solutions are applicable to alluvial channels of infinite length, initially at equilibrium followed by an arbitrary forcing function of either sediment transport or bed elevation imposed as an upstream boundary condition. The solutions have been used to predict aggradation in a channel due to constant overloading. Comparison of the results with available experimental data and with the solution obtained from a parabolic model is satisfactory. The present theory is significant conceptually since it provides valuable insight into the physical phenomenon as well as into the mathematical behavior of the solutions.