Analytical model for predicting the longitudinal profiles of velocities in a channel with a model vegetation patch

This paper proposes an analytical model for predicting the longitudinal profile of depth-averaged streamwise velocities in a channel with an emergent array of rigid cylinders. The governing equation of the analytical model was derived from the momentum equation and flow continuity equation. The longitudinal transect through a flume with a vegetation patch was divided into four regions based on two length scales of flow adjustment upstream of and inside the array, and analytical solutions were proposed for the four regions. Laboratory experiments demonstrated that the array length does not influence flow adjustments near the upstream edge of the array, so the model can predict the longitudinal profile of streamwise velocity for either short or long arrays. Twenty groups of velocity data from different sources were used to verify the proposed model. The predicted velocities agreed well with the measured velocities, indicating that the model is capable of predicting the longitudinal profiles of the velocity upstream of and inside a model patch. The predicted velocity profile can be further employed to estimate regions of enhanced or diminished deposition of fine sediment or organic matter inside model patches.