Analytical solution for depth-averaged velocity and boundary shear in a compound channel

Abstract

Estimation of streamwise depth-averaged velocity and boundary shear stress are important requisites for modelling of river flows associated with flood events. Recently, many methods have emerged to predict these flow variables with great accuracy, but they provide unsatisfactory results in shear layer regions. This paper presents an improved methodology to predict depth-averaged velocity and bed shear stress for a straight compound channel flow. An analytical solution to the depth-integrated turbulent form of the Navier–Stokes equation is obtained. The transverse shear stress in the mixing region is modelled using an effective eddy viscosity concept that contains horizontal coherent structures and three-dimensional bottom turbulence. The secondary flow term is modelled by considering the log-law profile for streamwise velocity and half cosine curve for the transverse velocity component. The analytical solution is successfully applied to a wide range of experimental compound channels and field cases. The efficacy of the present solution has been successfully tested by comparing with observed values.