Analytical model for streamwise velocity in vegetated channels

This paper presents a method for predicting the lateral distribution of depth-averaged streamwise velocity in straight prismatic open channels with emergent vegetation. The approach is fully consistent with the original Shiono and Knight method of analysis, and extends it to include the drag force due to vegetation, modelled as an additional momentum 'sink' term, with the blockage effect of the vegetation modelled by way of a porosity analogy. An analytical solution to the depth-integrated Reynolds-averaged Navier-Stokes equation is given which includes the effects of bed friction, drag force, lateral turbulence and secondary flows, governed by four coefficients f, C _D, λ and Γ respectively. The analytical results are shown to predict the lateral distributions of depth-averaged velocity well for three sets of experimental data: one for inbank flow in a partially vegetated channel and two for overbank flows in compound channels with partially vegetated floodplains. The analytical solution is also shown to give identical results to numerical simulations of the same governing Reynolds-averaged Navier-Stokes equation applied to some experiments undertaken in the UK Flood Channel Facility. The lateral distribution of bed shear stress is also obtained through the Darcy-Weisbach friction factor, thus providing a basis for modelling flood conveyance, fluvial processes and eco-environmental impacts in natural rivers.