Analytical model of the mean velocity distribution in an open channel with double-layered rigid vegetation

•Proposed an analytical model for open channel with double-layered rigid vegetation.•A power series was used to solve the momentum equations.•PIV measured data were used to validate the model and good agreement has been obtained. An analytical model for predicting the vertical distribution of mean streamwise velocity in an open channel with double-layered rigid vegetation is proposed. The double-layered model was constructed in a laboratory flume with an array of steel cylinders of two heights. For each vegetation layer (i.e., the short- or tall-vegetation layer), the flow is vertically separated into a lower vegetation zone and an upper vegetation zone, and corresponding momentum equations for each zone are formulated. For the lower vegetation zone, a uniform velocity was adopted since turbulent shear is relatively small and the Reynolds stress is ignored. For the upper vegetation zone, a power series was used to solve the momentum equations. For the free-water zone, a new expression was suggested to obtain a zero velocity gradient at the water surface instead of the traditional logarithmic velocity distribution. Good agreement between the analytical predictions and experimental data demonstrated the validity of the model.