Mathematical Simulation of Sediment Deposit in Estuaries

It is viewed as necessary and useful to devise a method which can be used to solve the problems of sediment deposit in estuaries more directly and completely. In this study, three basic equations have been extended to a more general case in which lateral inflows and various width of channel are considered. A solution of the problem has been obtained by Chang and Richards. In their research, three basic equations have been successfully reduced to two differential equations by assuming that the change in bed slope due to sediment deposit in a short period is insignificant compared with the original bed slope. Based upon these two differential equations, the method of characteristics has been used to solve the problem, and the computing procedures are divided into two parts: first, to compute the average velocity and depth of sediment-laden water, second, to estimate the deposition of sediment by using the continuity equation of sediment. In the following chapters, a solution of these three nonlinear differential equations is presented with mathematical analyses, computer approach and some notes in programming. The method of characteristics has been employed in this study. The analysis is based on the assumptions that the fluid has homogeneous density, the flow has uniform velocity in any cross section, and uniform diameters for sediment particles. It is also assumed that the bedform change due to the effect of bedload is neglected. A characteristic equation in the form of third order polynomial can be derived and solved by the numerical solution instead of graphical solution. The specific purposes of this research are to investigate the change of riverbed and water surface configurations due to sediment deposition in river estuaries, to extend the three basic equations for a more general case, and to establish a computer program for solving these equations by using the method of characteristics