A sheet flow or overland flow is simulated by the theory of laminar flow passing over a grassed slope with wood. The flow region is divided into two layers (vegetation layer & soil layer) or three layers (wood layer, vegetation layer & soil layer) according to the water depth. The Navier-Stokes equations are employed to govern the flow in the wood layer, and the Biot’s theory of poro-elasticity is applied to delineate the flow in the vegetation and soil layers. These equations are simplified, modified and nondimensionalized under different vegetation situations, and then solved
analytically. As a result, the velocity distributions are derived by a semi-analytical approach to understand the flow mechanism.
Key Words : Biot’s theory of poro-elasticity, vegetation flow, velocity distribution.