New hyperbolic tangent formula for mixing layer in vegetated flow

Abstract

Flow velocity profile in the vegetal mixing layer was investigated using data collected in the present experiments and those reported in the literature, which indicates that the inflection point of the velocity profile does not coincide with the middle position of the vegetal mixing layer. Aiming to solve this problem, the hyperbolic tangent formula that is applicable to the plane mixing layer is modified by revising the inflection point and applying different characteristic scales in the free flow and penetration regions. For the problem of predicting flow velocity on top of vegetation, we constructed a new calculation method for flow velocity on top of vegetation based on correlation analysis. The proposed formula yields significant improvements in representing measured velocity profiles in the vegetated open channel flows. In comparison with previous ones, the modified formula performs better in exhibiting the similarity of measured velocity profiles over a wide range of flow and vegetation conditions. The research results provide technical support for the high precision calculation of the vegetated mixing layer.