### Abstract

Known integrable models for ID 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.

Original language | English |
---|---|

Article number | W03526 |

Journal | Water Resources Research |

Volume | 46 |

Issue number | 3 |

DOIs | |

Publication status | Published - Dec 1 2010 |

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### All Science Journal Classification (ASJC) codes

- Water Science and Technology

### Cite this

*Water Resources Research*,

*46*(3), [W03526]. https://doi.org/10.1029/2009WR008181

**Analytical model of infiltration under constant-concentration boundary conditions.** / Triadis, Dimetre; Broadbridge, P.

Research output: Contribution to journal › Article

*Water Resources Research*, vol. 46, no. 3, W03526. https://doi.org/10.1029/2009WR008181

}

TY - JOUR

T1 - Analytical model of infiltration under constant-concentration boundary conditions

AU - Triadis, Dimetre

AU - Broadbridge, P.

PY - 2010/12/1

Y1 - 2010/12/1

N2 - Known integrable models for ID 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.

AB - Known integrable models for ID 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.

UR - http://www.scopus.com/inward/record.url?scp=78751615982&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78751615982&partnerID=8YFLogxK

U2 - 10.1029/2009WR008181

DO - 10.1029/2009WR008181

M3 - Article

AN - SCOPUS:78751615982

VL - 46

JO - Water Resources Research

JF - Water Resources Research

SN - 0043-1397

IS - 3

M1 - W03526

ER -