An analytical two-layer model for velocity distribution in open-channel flows with submerged flexible canopies considering multiply fluids mechanics

Abstract Submerged flexible vegetation such as reeds and sedge are quite common in rivers during flood seasons. Different from rigid aquatic vegetation like shurbs, flexible vegetation bends under the effect of streamwise flow, making the velocity profile even more complicated. This study aims to build an analytical model for predicting the vertical velocity profile in an open channel flow fully covered by submerged flexible vegetation whose projection area varies in vertical direction. A classical two-layer approach is applied which divides the flow into a vegetation layer and a free surface layer using the top of the vegetation patch as the boundary. For the vegetation layer, the vegetation-induced drag force is assumed to be proportion to the local streamwise velocity and projection area considering the influence of vegetation bending. In order to obtain the vertical velocity profile, width-averaged Navier-Stokes equation is solved with a first order closure scheme for the Reynolds stress. For the free surface layer, similar approach as the vegetation layer is applied while a wake function is added into the solution and the vegetation-induced drag force is considered to be zero in this layer. The average relative error between the results of current analytical model and experimental measurements is 4%–11%, indicating the applicability and accuracy of the model to predict the vertical velocity profile.