The Moving-Boundary Approach for Modeling 2-D Gravity-Driven Stable and Unstable Flow in Partially Wettable Soils

The moving-boundary approach, which has been successfully used to model stable and unstable 1-D flow in initially dry soils of various contact angles (Brindt & Wallach, 2017 https://doi.org/10.1002/2016WR019252), was extended here for 2-D flow. The wetting front is the plume perimeter that is partly formed by the capillary driving force, the remaining part by the combined capillary and gravity driving forces. The moving-boundary approach overcomes the limitation of the Richards equation for describing gravity-driven unstable flow with nonmonotonic water-content distribution. According to this approach, the 2-D flow domain is divided into two subdomains with a sharp change in fluid saturation between them—the wetting front (moving boundary). The 2-D Richards equation was solved for the subdomain behind the wetting front for a given flux boundary condition at the soil surface, while the location of the other boundary, for which a no-flux condition is imposed, was part of the solution. The moving-boundary solution was used after verification to demonstrate the synergistic effect of contact angle and incoming flux on flow stability and its associated plume shapes. The contact angle that hinders spontaneous invasion of the dry pores decreases the water-entry capillary pressure, ψ_we, while the flux-dependent dynamic water-entry value, ψ_wed, is even lower, both inducing water accumulation behind the wetting front (saturation overshoot). This innovative physically based model for the 2-D unsaturated flow problem for an initially dry soil of zero and nonzero contact angle using the moving-boundary approach fulfills several criteria raised by researchers to adequately describe gravity-driven unstable flow.