Applicability of St. Venant Equations for Two‐Dimensional Overland Flows over Rough Infiltrating Surfaces

Abstract

The physics‐based modeling of overland flow is accomplished through the numerical solution of the St. Venant equations. One of the assumptions used in the derivation of the St. Venant equations is that of gradually varied flow. In many instances, simpler forms of the flow equations (the kinematic and diffusion wave models) are utilized to save computational effort. The flow equations for all these models are nonlinear and frequently fail to converge when applied to surfaces with highly irregular microtopography, which yields abrupt changes in slopes at adjacent nodes. Since the flow equations perceive the flow profile as a thin sheet, the microtopography needs to be replaced by a smoother surface for computational purposes. Comparison of numerical solutions of the flow models with observed results over experimental hillslopes is satisfactory. Replacing the spatially varying microtopography with an average constant slope cause no significant change in the outflow hydrograph, which is a spatially integrated property. However, significant differences are obtained for the steady‐state local flow depths and velocities in the solution of the St. Venant equations over varying and smooth topographies. These results have important ramifications in modeling the transport of solutes or sediments by shallow surface flows.