Analytical solution for vertical profile of streamwise velocity in open-channel flow with submerged vegetation

A three-zone model was constructed and applied to study vertical profiles of streamwise velocity in steady uniform, open-channel flows with submerged vegetation. Three zones are examined-lower vegetation, upper vegetation and non-vegetated. Dominant forces acting on the water body were mainly gravity, vegetation drag and Reynolds stress. The latter was estimated by mixing length theory. A power series method was used to solve the governing differential equation of the upper vegetation zone. Other governing equations for the remaining two zones were directly solved analytically, deriving formulas for calculating the streamwise velocities. Values calculated with the formulas agreed well with measured experimental data, which demonstrates the practical applicability of the model.