Mathematical Model for The Flow with Submerged and Emerged Rigid Vegetation

The article summarizes previous studies on the flow in open channels with rigid vegetation, and constructs a mathematical model for submerged and emerged rigid vegetation. The model involves the forces balance in the control volume in one-dimensional steady uniform flow. For submerged vegetation, the whole flow is divided into four regions: external region, upper vegetated region, transition region and viscous region. According to the Karman similarity theory, the article improves the mixing length expression, and then gives an analytical solution to predict the vertical distribution of stream-wise velocity in the external region. For emerged vegetation, the flow is divided into two region: outer region and viscous region. In the two circumstances, the thicknesses of each region are determined respectively. The comparison between the calculated results and our experimental data and other researchers' data proves that the proposed model is effective.