A Multi-Mechanism Model for the Velocity Profile in Vegetated Open-Channel Flows

Velocity profiles in vegetated channels reflect multiple mechanisms of flow-vegetation interactions and determine bulk flow velocity, and hence the overall hydraulic resistance. Most existing velocity profile models are based on single physical concepts that are used for theoretical considerations and data interpretation. However, measured velocity profiles in vegetated flows show that the use of a single concept is not only insufficient to explain all transport and turbulence production mechanisms, but also does not cover all flow-vegetation scenarios. To address these issues a number of researchers have expressed velocity profiles as a set of linked segments with different approximations, i.e., within each non-overlapping segment a different physical concept is applied. While such segmented models have improved our understanding of flow-vegetation interactions, new conceptual approaches and analytical formulations describing the flow structure are still required. In this paper we propose a new approach where a vertical velocity profile in vegetated channels is modeled as a linear superposition of four concepts applied over the whole flow depth: (1) uniform velocity distribution; (2) mixing layer analogy concept and associated hyperbolic tangent profile; (3) boundary layer concept and its logarithmic profile; and (4) the wake function concept. Using this approach, a new analytical model is developed. The proposed analytical expression combines these concepts simultaneously over the whole flow depth allowing significant overlaps of momentum transport and turbulence production mechanisms. The model is successfully tested using extensive laboratory experiments covering wide ranges of background flow and vegetation parameters.