A Direct Analytical Approach for Solving Surface and Subsurface Water Flow on a Hillslope

10.29417/JCSWC.201212_43(4).0003

Ping-Cheng Hsieh；Ching-Ya Tang；Siou-Yi Hu

Surface water ； laminar flow ； vegetation ； porous media flow ； poroelasticity

中華水土保持學報

43卷4期（2012 / 12 / 01）

302 - 311

英文

Surface water flow passing over unplanted ground and vegetated ground is delineated analytically. The velocity distribution of surface and subsurface water flow is directly solved by the simplified Navier-Stokes equations and Biot's theory of poroelasticity. The velocity will increase with increasing water depth, slope and porosity of the vegetation-layer. Higher permeabilities of the soil layer will increase the velocity inside the soil, but it has little influence on the velocity above the ground. The mean velocity of the overland flow passing over a vegetated or non-vegetated hillslope is compared with those calculated by the Darcy-Weisbach (D-W) formula and the kinematic-wave (K-W) equation. For the case of unplanted ground, the result of the proposed approach is less than that of the K-W equation but larger than that of the D-W formula. For the case of emergent vegetation, the mean velocity of the D-W formula reaches its minimum when the porosity of the vegetation layer is larger than 0.94 and the surface water depth is less than 0.05 m.