A novel semi-analytical approach for non-uniform vegetated flows

• Non-uniform flow and drag force through the grass were studied semi-analytically.
• Max. shear stress exists either at the top of the grass layer or on the ground.
• An inflection point appears near the interface for the submerged case as expected.
• The flow profile of the mixed type grass is successfully and smoothly plotted.
• A new approach to better understand the mechanism of vegetated flows was proposed.

In this paper a semi-analytical approach is proposed to understand the mechanism by which a non-uniform vegetated flowpasses over a finite thick soil layer covered with grass. The flow region is divided into three layers: a homogenous water layer, a mixed water-grass layer, and a finite thick soil layer (hereafter referred to as the water layer, the grass layer, and the soil layer). The flow of the water layer is governed by the Navier–Stokes equations. Both the grass and soil layers are regarded as porous media and the Biot’s theory of poroelasticity is applied to the porous medium flow. The semi-closed solutions are then obtained by the Runge–Kutta method. The drag force induced by the flow through the grass layer and the flow profiles of three patterns: submerged grass, emergent grass and mixed type are also discussed.