A Numerical Model for Calculating the Distributions of Velocity and Boundary Shear Stress Across Irregular Straight Open Channels

A model is presented for calculating the distributions of velocity and boundary shear stress across irregular straight open channels. A turbulent kinetic energy transport equation and a two‐dimensional ramp function for the turbulent length scale provide turbulence closure. A modified sigma transformation maps the channel cross section onto a rectangular domain; the transformed equations are solved by a simple finite difference algorithm. Velocity profiles generated by the model are logarithmic close to the bed, but in the core of the flow, predicted velocities follow a wake profile similar to that observed experimentally. The boundary shear stresses calculated by the model for smooth one‐dimensional flows are accurate to within 0.02%. The model also reproduces flow and boundary shear stress data for smooth rectangular and trapezoidal laboratory channels; the average boundary shear stress is calculated to within about 1%, and the distributions of velocity and shear stress are similar to those obtained from laboratory measurements. Local errors are caused by ignoring weak secondary currents and by using a simplistic symmetry assumption for the boundary condition at the water's surface. The model overestimates the discharge by an average of 8%; this error probably occurs because the model ignores the resistance due to secondary currents.