Analytical solution of transient flow in a sloping soil layer with recharge

Abstract

An analytical solution of planar flow in a sloping soil layer described by the linearized extended Boussinesq equation is presented. The solution consists of the sum of steady-state and transient-series solutions, the latter in a separation-of-variables form, and can satisfy an arbitrary initial condition via collocation; this feature reduces the number of series terms, making the solution efficient. Key parameter is the dimensionless linearization depth ηo(R)R, being the dimensionless recharge. The variable ηo(R), not the slope, characterizes the flow as kinematic or diffusive, and R = 0.2 demarcates the two regimes. The transient series converges rapidly for large ηo (large R, near-diffusive flow) and slowly as ηo → 0 (kinematic flow). The quasi-steady (QS) state method of Verhoest & Troch is also analysed and it is shown that the QS depth profiles approximate the transient ones well, only if Δt exceeds a system-dependent transition time between flow states (possibly >>1 day). In an application example for a 30-day recharge series, the QS solution differs from the transient one by as much as 20% (RMSE = 15%), does not track recharge changes as well and fails to conserve mass. Copyright © 2006 IAHS Press.