A multiple-fluids-mechanics-based model of velocity profiles in currents with submerged vegetation

Abstract

Submerged aquatic vegetation can provide a habitat and food for marine and river organisms, and it has the ecological effect of purifying water by absorbing harmful substances. Therefore, it plays an important role in the maintenance, restoration, and improvement of marine and river ecosystems. Hydrodynamic problems caused by submerged vegetation have been a matter of wide concern. According to the distribution of submerged vegetation, the flow can be divided into three layers in the vertical direction: uniform, mixing, and logarithmic layers. This paper proposes an analytical model for the vertical distribution of longitudinal velocity in open-channel flows with submerged vegetation. A concept of velocity superimposition is applied in mixing and logarithmic layers. The velocity inside the vegetated layer can be solved by the balance between the drag force and bed gradient. The velocity difference between the vegetated layer and the free surface layer results in the formation of a mixing layer near the top of the vegetation. Flow at the junction between the vegetation and free surface layers is mainly controlled by the vortices in the mixing layer. The velocity in the mixing layer is commonly described by a hyperbolic tangent formula. The logarithmic distribution formula is applied to the free surface layer, where the velocity without effect arising from vortices is similar to the open-channel flow. The concept of the wake function is introduced to modify the distribution of velocity in the free surface layer. The longitudinal velocities from the theoretical model are compared to the measured velocities in the literature. The theoretical velocities agree well with the measured values in the flows with submerged vegetation, proving that the theoretical model proposed here can successfully predict the vertical distribution of velocity and has extensive adaptability.