An Analytical Solution to Predict the Distribution of Streamwise Flow Velocity in an Ecological River with Submerged Vegetation

Abstract

Aquatic submerged vegetation is widespread in rivers. The transverse distribution of flow velocity in rivers is altered because of the vegetation. Based on the vegetation coverage, the cross-section of the ecological channels can be divided into the non-vegetated area and the vegetated area. In the vegetated area, we defined two depth-averaged velocities, which included the water depth-averaged velocity, and the vegetation height-averaged velocity. In this study, we optimized the ratio of these two depth-averaged velocities, and used this velocity ratio in the Navier–Stokes equation to predict the lateral distribution of longitudinal velocity in the open channel that was partially covered by submerged vegetation. Based on the Navier–Stokes equations, the term “vegetation resistance” was introduced in the vegetated area. The equations for the transverse eddy viscosity coefficient ξ, friction coefficient f, drag force coefficient Cd, and porosity α were used for both the non-vegetated area and the vegetated area, and the range of the depth-averaged secondary flow coefficient was investigated. An analytical solution for predicting the transverse distribution of the water depth-averaged streamwise velocity was obtained in channels that were partially covered by submerged vegetation, which was experimentally verified in previous studies. Additionally, the improved ratio proposed here was compared to previous ratios from other studies. Our findings showed that the ratio in this study could perform velocity prediction more effectively in the partially covered vegetated channel, with a maximum average relative error of 4.77%. The improved ratio model reduced the number of parameters, which introduced the diameter of the vegetation, the amount of vegetation per unit area, and the flow depth. This theoretical ratio lays the foundation for analyzing the flow structure of submerged vegetation.

Keywords

• submerged vegetation
• water depth-averaged streamwise velocity
• Navier–Stokes equations
• secondary flow coefficient
• analytical solution
• velocity ratio