Modeling Depth-Averaged Velocity and Boundary Shear in Trapezoidal Channels with Secondary Flows

The Shiono and Knight method (SKM) offers a new approach to calculating the lateral distributions of depth-averaged velocity and boundary shear stress for flows in straight prismatic channels. It accounts for bed shear, lateral shear, and secondary flow effects via 3 coefficients— $f,\lambda$ , and $\Gamma$ —thus incorporating some key 3D flow feature into a lateral distribution model for streamwise motion. The SKM incorporates the effects of secondary flows by specifying an appropriate value for the $\Gamma$ parameter depending on the sense of direction of the secondary flows, commensurate with the derivative of the term $H\rho (UV{)}_d$ . The values of the transverse velocities, $V$ , have been shown to be consistent with observation. A wide range of boundary shear stress data for trapezoidal channels from different sources has been used to validate the model. The accuracy of the predictions is good, despite the simplicity of the model, although some calibration problems remain. The SKM thus offers an alternative methodology to the more traditional computational fluid dynamics (CFD) approach, giving velocities and boundary shear stress for practical problems, but at much less computational effort than CFD.