Direct Analytical Solution of Turbulent Surface Water Flow on a Slope

Abstract

A direct analytical approach is proposed to study the turbulent surface water flow on a slope. Both unplanted ground and grassed ground are investigated by dividing the flow field into two layers—homogenous water layer/vegetation layer and permeable soil layer, respectively. The soil and vegetation layers are regarded as porous media, and Biot’s poroelastic theory is applied. The effect of vegetation on flow velocity is also analyzed. As the Reynolds stresses become larger, the turbulent strength increases, and the velocity distributions become more uniform. The average velocity is compared with that calculated by Manning’s formula and the kinematic-wave equation. The result shows that the average velocity using the kinematic-wave equation is the highest, and the present solution is the smallest for both cases.