Analytical solutions for water flow passing over a vegetal area

This study is aimed at investigating the vertical velocity profile of flow passing over a vegetal area by an analytical approach. The soil ground is considered as pervious and thus non-zero velocity at the ground surface can be estimated. The soil and vegetation layers are regarded as homogeneous and isotropic porous media. Therefore the solution of the flow can be obtained by applying the theory of turbulent flow and Biot’s theory of poroelasticity after dividing the flow field into three layers: homogenous water, vegetation and pervious soil. The velocity distribution is compared with the experimental data of [Rowiński PM, Kubrak J. A mixing-length model for predicting vertical velocity distribution on flows through emergent vegetation. J Hydrol Sci 2002;47(6):893–904] to show its validity. In addition, five dimensionless parameters denoting the variation of slope, permeability of soil, Reynolds stress, density of vegetation, and relative height of vegetation are proposed to reveal their effects on the surface water flow. The analytical solutions of flow velocity can also be simplified into simpler expressions to describe the flow passing over a non-vegetated area.