NONLINEAR STABILITY ANALYSIS OF SHALLOW OPEN-CHANNEL FLOW WITH LATERAL VELOCITY GRADIENTS

Abstract

The turbulent flow in a wide rectangular open-channel with lateral vegetation is studied by performing a weakly nonlinear stability analysis. The vegetation acts as a source of drag forces which provide resistance to the flow, such that there is an inflection point in the depth-averaged streamwise velocity. The generated instabilities may grow into discrete horizontal vortices centred at the edge of the vegetated region. The growth rate expansion method is applied with the multiple scale perturbation technique to the governing normalized Navier-Stokes equations. The small perturbation is added to a parameter related to the vegetation density.