Hydraulic Analysis of a Two-Dimensional Water Flow Down a Hillslope

Abstract

In this study, the authors describe the hydraulic mechanism of a 2D water flow down a slope. The surface water flowed in Layer 1, whereas the subsurface water flow was in Layer 2. Layer 2 is regarded as an isotropic porous medium such that the flow velocity on the ground surface is nonzero. The Navier-Stokes equation and the laminar model based on Biot’s poroelastic theory were applied to the flow motion in Layers 1 and 2, respectively. Additionally, the authors formulated the problem by considering the vertical velocity in the momentum equation. With the hypothetical velocity type and appropriate boundary conditions, the authors derived some nonlinear ordinary differential equations and solved them by taking the differential transform method (DTM). The authors delineated the distributions of horizontal velocity, vertical velocity, and shear stresses in both layers, and the horizontal velocity of the surface water flow was compared with previous studies.