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Analytical model of infiltration under constant‐concentration boundary conditions
Author(s) -
Triadis D.,
Broadbridge P.
Publication year - 2010
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2009wr008181
Subject(s) - sorptivity , infiltration (hvac) , mathematics , hydraulic conductivity , power series , thermal diffusivity , extrapolation , boundary value problem , mathematical analysis , soil water , soil science , thermodynamics , physics , geology , compressive strength
Known integrable models for 1D flow in unsaturated soil have a rescaled soil water diffusivity that is either constant or proportional to C ( C − 1)/( C − Θ) 2 , where Θ is the degree of saturation and C > 1 is constant. With a wider more realistic range of hydraulic conductivity functions than has been used in this context before, a formal series solution is developed for infiltration, subject to constant‐concentration boundary conditions. A readily programmed iteration algorithm, applicable for any value of C , is used to construct many coefficients of the infiltration series without requiring any numerical integration. In particular, for either C − 1 small or 1/ C small, several infiltration series coefficients are constructed as formal power series in C − 1 or in 1/ C , for which we construct a number of terms explicitly. In the limit as the diffusivity approaches a delta function, the infiltration coefficients are obtained in simpler closed form. All but the sorptivity depend on the form of the conductivity function.