Models for the Turbulent Diffusion Terms of Shallow Water Equations

Abstract

The analysis of three different approximations of the turbulent diffusion terms, widely used to simulate shallow water flows, is carried out both analytically and experimentally. Based on the eddy viscosity concept, the terms are solved for steady, uniform, turbulent flow in a simplified geometry, which may represent a tidal estuary or a compound channel. It is shown that, although the three approximations are identical in constant depth, they behave differently if strong depth gradients exist and, consequently, the transverse velocity profile obtained varies depending on the turbulence term used. It is also shown that the relative depth (flood plain depth-to-main channel depth ratio) has an important influence on the lateral momentum transfer and, consequently, depending on the approximation adopted, different dimensionless eddy viscosity coefficient λ values must be used to best fit the experimental data. A tentative relationship between the relative depth and the dimensionless eddy viscosity coefficient is presented for each expression. Comparison of analytical results with experimental data shows that not all the widely used expressions for the turbulence terms can adequately represent the velocity profile if strong depth gradients exist.