Analytical Models for Velocity Distributions in Open Channel Flows

Various models for the analytical solution to the depth-integrated Navier-Stokes equations, applied to open channel flows, are discussed. These models include the effects of bed friction, lateral turbulence and secondary flows. The model developed by Shiono and Knight (1988, 1991) is compared with those by Ervine et al. (2000) and Castanedo et al. (2005) through numerical experiments on both simple and compound channels. These tests show that the impact of the secondary flow term on the results is significant. It is also shown that the dimensionless eddy viscosity coefficient has less influence on the results than the secondary flow terms for overbank flows, but is important for inbank flows. A comparison of the analytical results with experimental data shows that the model by Shiono and Knight produces well velocity distributions within open channels of various prismatic shapes.