Experiments, analytical and HYDRUS2D modeling of steady jet of quasi-normal surface flow in rectangular channel coupled with vertical seepage: Vedernikov-Riesenkampf's legacy revisited

Channels are widely used for conveying natural flash floods or managed aquifer recharge (MAR) released treated wastewater. Adequate models are needed for describing the interaction between hydraulics of surface flow downslope the channel and vertical seepage into a porous bed for evaluation of the depth of water and the length to which surface water “jet” propagates over a porous bed. Experiments with surface “jets” (consumed by bed infiltration) are compared with numerical and analytical modeling of these coupled flows. In the field (Al-Hail site, Oman), at a pedestal and slope of a dune, two rectangular trenches had a sand bed and a mild and steep slope S (3° and 25°, correspondingly). After applying constant discharges at the inlet of the trenches, the length, L, of the water “jets” propagating until complete extinction has been measured. The wetting front into the subjacent sand has been detected by measuring the volumetric soil moisture content at different depths in an excavation, immediately after termination of discharging the surface water. Analytically (by the hodograph method), 2-D steady phreatic seepage flow from a rectangular channel was examined as a special case of Vedernikov's solution for a soil without capillarity. Since the depth of water was small, the Riesenkampf analytical solution, involving capillarity in the tension-saturated flanks of the channel, has been also utilized. Numerically, Richard's equation has been solved by a finite element method, HYDRUS2D for arbitrary soils. The boundary condition was a hydrostatic pressure head along the wetted perimeters of the channels with water depth gradually dropping downslope. Coupling of surface and subsurface flows has been done by the “kinematic waves” approximation with Manning's friction slope equal to S. In the ODE for conservation of mass, the sink term (infiltration) was computed by either HYDRUS or analytical solution. The corresponding boundary value problem was solved by computer algebra routines.