Seimanylitical Model for Shear Stress Distribution in Simple and Compound Open Channels

Semianalytical equations were derived for distribution of shear stress in straight open channels with rectangular, trapezoidal, and compound cross sections. These equations are based on a simplified streamwise vorticity equation that includes secondary Reynolds stresses. Reynolds stresses were then modeled and their different terms were evaluated based on the work of previous researchers and experimental data. Substitution of these terms into the simplified vorticity equation yielded the relative shear stress distribution equation along the width of different channel cross sections. In compound channels the effect of additional secondary flows due to the shear layer between the main channel and the flood plain were also considered. Comparisons between predictions of the model and experimental data, predictions of other analytical or three dimensional numerical models with advanced turbulent closures, were made with good agreement.