Propagation of Nonlinear Flood Waves in Rivers

Abstract

AbstractThe propagation of flood waves in rivers is governed by the Saint Venant equations. Under certain simplifying assumptions, these nonlinear equations have been solved numerically via computationally intensive, specialized software. There is a cogent need for simple analytical solutions for preliminary analyses. In this paper, new approximate analytical solutions to the nonlinear kinematic wave equation and the nonlinear dynamic wave equations in rivers are presented. The solutions have been derived by combining Adomian’s decomposition method (ADM), the method of characteristics, the concept of double decomposition, and successive approximation. The new solutions compare favorably with independent simulations using the modified finite-element method and field data at the Schuylkill River near Philadelphia. The time to peak calculated by the analytical and numerical methods is in excellent agreement. There appears to be some minor differences in the peak magnitude and recession limb, possibly because...