Abstract
A predictive theory to study the nonlinear development of the perturbations in a channel with a lateral gradient in the streamwise velocity due to the presence of bank vegetation is presented. The ratio between the undisturbed parallel velocities in the vegetated and non-vegetated zones is taken as the expanded parameter at the weakly nonlinear stability analysis, along with its corresponding wavenumber at a critical condition where the perturbations nor grow nor decay. In most cases evaluated herein, we have supercritical bifurcation, where the amplitude of the perturbations is found to reach an upper bound as time tends to infinity. We find reasonable agreement between predicted and experimental results for the time-averaged velocity profile, kinematic eddy viscosity, shear layer width and maximum friction velocity.
