Entropy-based design approach of threshold alluvial channels

A new approach has been developed for designing the shape and dimensions of the cross section of a straight threshold channel based on the concepts of entropy and probability. A formula for the lateral distribution of transverse slopes, and hence the cross-sectional bank profile, was derived by the entropy-maximisation principle and the calculus of variations. The bank profile is a new type of simple parabolic curve. The results of numerical experiments based on the approach of boundary shear stress distribution support the conclusion that the entropy-based channel bank profile is at threshold. Bank profile equations are coupled with an appropriate frictional relationship to obtain a new design method. Channel dimensions and bank profiles predicted by this method are compared with those given by other design methods. The predicted channel dimensions are in reasonable agreement with laboratory experimental data.