A Semicoupled Shallow-Water Model for Vertical Velocity Distribution in an Open Channel with Submerged Flexible Vegetation

Abstract

This study detailed a novel semicoupled method for estimating the three-dimensional vertical velocity profile in an open channel with submerged flexible vegetation. A modified form of the two-dimensional shallow water equations coupled with the drag forces of the vegetation was derived by balancing the flux gradient and the source term. The bending profile of the flexible stems of different flow events was calculated based on the large cantilever beam theory. The vertical velocity profile in the free water and vegetation layers was estimated using Shannon’s entropy and Reynold’s stress equation theory, respectively. The derived semicoupled model was tested to replicate two popular laboratory flume experiments. The results showed that the model accurately predicted the velocity profiles under different flow conditions and patch density. The R2 values of 0.76 and 0.81 indicate that the proposed model is well established and can be applied in complex flow scenarios.