Motion of wetting fronts moving into partially pre-wet soil

Advances in Water Resources

Volumn 28, Issue 10 SPEC. ISS., 2005, Pages 1133-1141

  Witelski, Thomas P ^a  

^a DUKE UNIVERSITY   (United States)

Author keywords

Richards' equation; Traveling waves; Vertical infiltration; Wetting fronts

Indexed keywords

APPROXIMATION THEORY; BOUNDARY VALUE PROBLEMS; MATHEMATICAL MODELS; MOISTURE; SOILS; WETTING;

RICHARDS EQUATION; TRAVELING WAVES; VERTICAL INFILTRATION; WETTING FRONTS;

INFILTRATION;

ADVECTION-DIFFUSION EQUATION; INFILTRATION; RICHARDS EQUATION; WETTING FRONT;

EID: 24644499038     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2004.06.006     Document Type: Article

References (35)

1. M. Abramowitz I.A. Stegun editors. Handbook of mathematical functions with formulas, graphs, and mathematical tables 1992 Dover Publications Inc. New York
2. G.I. Barenblatt Scaling, self-similarity, and intermediate asymptotics 1996 Cambridge University Press New York
3. D.A. Barry J.-Y. Parlange J.L. Starr Numerical analysis of the precursor effect Soil Sci 143 5 1987 309-317
4. H.A. Basha Burgers' equation: A general nonlinear solution of infiltration and redistribution Water Resour Res 38 11 2002 1247
5. J. Bear Dynamics of fluids in porous media 1972 American Elsevier New York
6. P. Broadbridge C. Rogers Exact solutions for vertical drainage and redistribution in soils J Eng Math 24 1 1990 25-43
7. P. Broadbridge I. White Constant rate rainfall infiltration: A versatile nonlinear model 1. analytic solution Water Resour Res 24 1 1988 145-154
8. H.S. Carslaw J.C. Jaeger Conduction of heat in solids 2nd ed. 1959 Clarendon Press Oxford
9. B.H. Gilding Qualitative mathematical analysis of the Richards equation Transport Porous Med 5 1991 651-666
10. R.E. Grundy Asymptotic solution of a model nonlinear convective diffusion equation IMA J Appl Math 31 2 1983 121-137
11. W.L. Hogarth J.-Y. Parlange J. Sprintall R. Haverkamp M.B. Parlange Addendum to interaction of wetting fronts with an impervious surface Transport Porous Med 21 1995 95-99
12. W.L. Hogarth J.-Y. Parlange J.L. Starr Simultaneous nonlinear irreversible reaction and movement of solutes in soils Soil Sci 154 6 1992 473-481
13. G. Kleinstein L. Ting Optimum one-term solutions for heat conduction problems Z Angew Math Mech 51 1971 1-16
14. F.J. Leij M.Th. Van Genuchten Analytical modeling of nonaqueous phase liquid dissolution with Green's functions Transport Porous Med 38 1-2 2000 141-166
15. J.D. Logan Transport modeling in hydrogeochemical systems Interdisciplinary applied mathematics Vol. 15 2001 Springer-Verlag New York
16. J.C. Miller A.J. Bernoff Rates on convergence to self-similar solutions of Burgers' equation Stud Appl Math 111 1 2003 29-40
17. A. Ogata R.B. Banks A solution of the differential equation of longitudinal dispersion in porous medium US Geol Survey Prof Paper 411-A 1961 9
18. J.-Y. Parlange Theory of water movement in soils: 8 one-dimensional infiltration with constant flux at the surface Soil Sci 114 1 1972 1-4
19. J.-Y. Parlange W.L. Hogarth C. Fuentes J. Sprintall R. Haverkamp D. Elrick et al. Interaction of wetting fronts with an impervious surface-longer time behavior Transport Porous Med 17 3 1994 249-256
20. J.-Y. Parlange W.L. Hogarth C. Fuentes J. Sprintall R. Haverkamp D. Elrick et al. Superposition principle for short-term solutions of Richards equation - application to the interaction of wetting fronts with an impervious surface Transport Porous Med 17 3 1994 239-247
21. J.-.Y. Parlange I. Lisle R.D. Braddock The three-parameter infiltration equation Soil Sci 133 6 1982 337-341
22. J.-Y. Parlange D.A. Lockington R.D. Braddock Nonlinear diffusion in a finite layer Bull Aust Math Soc 26 1982 249-261
23. J.-Y. Parlange J.L. Starr Dispersion in soil columns: Effect of boundary conditions and irreversible reactions Soil Sci Soc Am J 42 1978 15-18
24. J.R. Philip The theory of infiltration: 2 the profile at infinity Soil Sci 83 1957 435-448
25. Ravi V, Williams JR. Estimation of infiltration rate in the vadose zone: compilation of simple mathematical models, volume I. Technical report, United States Environmental Protection Agency, 1998. http://www.epa/gov/ada/download/reports/infiltvol.pdf
26. G.C. Sander J.-Y. Parlange V. Kühnel W.L. Hogarth D. Lockington J.P.J. O'Kane Exact nonlinear solution for constant flux infiltration J Hydrol 97 1988 341-346
27. J.L. Starr J.-Y. Parlange Dispersion in soil columns: The snow plow effect Soil Sci Soc Am J 43 1979 448-450
28. M.T. van Genuchten J.C. Parker Boundary conditions for displacement experiments through short laboratory soil columns Soil Sci Soc Am J 48 1984 703-708
29. M.Th. Van Genuchten Analytical solutions for chemical transport with simultaneous adsorption, zero-order production, and first-order decay J Hydrol 49 1981 213-233
30. V. Vanaja P.L. Sachdev Asymptotic solutions of a generalized burgers equation Quart Appl Math 50 4 1992 627-640
31. G.B. Whitham Linear and nonlinear waves 1974 Wiley New York
32. T.P. Witelski Perturbation analysis for wetting fronts in Richards' equation Transport Porous Med 27 1997 121-134
33. T.P. Witelski Horizontal infiltration into wet soil Water Resour Res 34 7 1998 216-222
34. T.P. Witelski Intermediate asymptotics for Richards' equation in a finite layer J Eng Math 45 3-4 2003 379-399
35. T.P. Witelski A.J. Bernoff Self-similar asymptotics for linear and nonlinear diffusion equations Stud Appl Math 100 2 1998 153-193