Date of Award:


Document Type:


Degree Name:

Doctor of Philosophy (PhD)


Civil and Environmental Engineering


J. Paul Riley


The movement of translatory waves over an erodible stream has a critical influence on the time of rise of the hydrograph which, in turn, affects the stability of the stream channel. In the present study, the movement of these flood waves is described by the one-dimensional equations of continuity and motion which are obtained by the space integration of the three-dimensional equation of continuity and Reynolds equations. The flow of suspended sediment is described by a one-dimensional dispersion equation which is derived from a three-dimensional equation of conservation of solid mass in the flow. With some modifications the one-dimensional dispersion equation is used to describe the scouring of the stream bed. Then the suspended sediment model is connected to the bed scouring model by a stochastic model which describes the bed load and the sediment transfer between the suspended sediment state and the immobile bed state. The stochastic model consists of a set of nine Kolmogorov differential equations for the probabilities of sediment transfer between different states in which a sediment particle may be.

To obtain a high-accuracy approximation in the solution of the one-dimensional equations of continuity and motion, the one-step Lax-Wendroff numerical scheme is adopted. The Kolmogrov differential equations are solved directly by means of an analog computer. An analytical investigation of the stability of the approximation scheme is performed. The simulation of the model is done on a hybrid computer by incorporating into the entire model various model components and testing the effects of each component on the whole model and on the other components to see its behavior.