SEARCH

SEARCH BY CITATION

References

  • Alt, W., S. Luckhaus, and A. Visintin, On nonstationary flow through porous media, Ann. Mat. Pura Appl., 136, 303316, 1984.
  • Baker, R. S., and D. Hillel, Laboratory tests of a theory of fingering during infiltration into layered soils, Soil Sci. Soc. Am. J., 54, 2030, 1990.
  • Barenblatt, G. I., Scaling, Self-Similarity, and Intermediate Asymptotics, Cambridge Texts Appl. Math., vol. 14, Cambridge Univ. Press, New York, 1996.
  • Carmona, R. A., and J. Lacroix, Spectral theory of random Schrödinger operators, Birkhauser, Boston, 1999.
  • Chakka, K. B., and C. L. Munster, Atrazine and nitrate transport to the brazos river floodplain aquifer, Trans. Am. Soc. Agric. Eng., 40, 615621, 1997.
  • Cuesta, C., C. J. V. Duijn, and J. Hulshof, Infiltration in porous media with dynamic capillary pressure: Travelling waves, Eur. J. Appl. Math., 11, 381397, 2000.
  • Dautov, R. Z., A. G. Egorov, J. L. Nieber, and A. Y. Sheshukov, Simulation of two-dimensional gravity-driven unstable flow, in Computational Methods in Water Resources, Elsevier Ser. Dev. Water Sci., vol. 47, edited by S. M. Hassanizadeh et al., pp. 916, Elsevier Sci., New York, 2002.
  • Diment, G. A., and K. K. Watson, Stability analysis of water movement in unsaturated porous materials, 2, Numerical studies, Water Resour. Res., 19, 10021010, 1983.
  • Diment, G. A., K. K. Watson, and P. J. Blennerhassett, Stability analysis of water movement in unsaturated porous materials, 1, Theoretical considerations, Water Resour. Res., 18, 12451254, 1982.
  • Du, X., T. Yao, W. D. Stone, and J. M. H. Hendrickx, Stability analysis of the unsaturated water flow equation, 1, Mathematical derivation, Water Resour. Res., 37, 18691874, 2001.
  • Egorov, A. G., R. Z. Dautov, J. L. Nieber, and A. Y. Sheshukov, Stability analysis of traveling wave solution for gravity-driven flow, in Computational Methods in Water Resources, Elsevier Ser. Dev. Water Sci., vol. 47, edited by S. M. Hassanizadeh et al., pp. 121128, Elsevier Sci., New York, 2002.
  • Eliassi, M., and R. J. Glass, On the continuum-scale modeling of gravity-driven fingers in unsaturated porous media: The inadequacy of the Richards equation with standard monotonic constitutive relations and hysteretic equations of state, Water Resour. Res., 37, 20192035, 2001.
  • Elliott, J. A., A. J. Cessna, K. B. Best, W. Nicholaichuk, and L. C. Tollefson, Leaching and preferential flow of lopyralid under irrigation: Field observations and simulation modeling, J. Environ. Qual., 27, 124131, 1998.
  • Glass, R. J., T. S. Steenhuis, and J.-Y. Parlange, Mechanism for finger persistence in unsaturated, porous media: Theory and verification, Soil Sci., 148, 6070, 1989.
  • Gray, W. G., and S. M. Hassanizadeh, Unsaturated flow theory including interfacial phenomena, Water Resour. Res., 27, 18551863, 1991.
  • Green, W. H., and G. A. Ampt, Studies in soil physics. 1. The flow of air and water through soils, J. Agric. Sci., 4, 124, 1911.
  • Hassanizadeh, S. M., and W. G. Gray, Thermodynamic basis of capillary pressure in porous media, Water Resour. Res., 29, 33893405, 1993.
  • Hillel, D., and R. S. Baker, A descriptive theory of fingering during infiltration into layered soils, Soil Sci., 146, 5156, 1988.
  • Isensee, A. R., R. G. Nash, and C. S. Helling, Effect of conventional vs. no-tillage on pesticide leaching to shallow groundwater, J. Environ. Qual., 19, 434440, 1990.
  • Jarvis, N., Modeling the impact of preferential flow on nonpoint source pollution, Ann Arbor Press, Chelsea, Michigan, 1998.
  • Joseph, D. D., Stability of Fluid Motions, vol. 1, Springer-Verlag, New York, 1976.
  • Ju, S.-H., and K.-J. S. Kung, Steady-state funnel flow: Its characteristics and impact on modeling, Soil Sci. Soc. Am. J., 61, 416427, 1997.
  • Kapoor, V., Criterion for instability of steady-state unsaturated flows, Transp. Porous Media, 25, 313334, 1996.
  • Kung, K. J. S., Preferential flow in a sandy vadose zone soil, 2. Mechanism and implications, Geoderma, 46, 5971, 1990.
  • Lissey, A., Depression-focused transient groundwater flow patterns in manitoba, Geol. Assoc. Can. Spec. Pap., 9, 333341, 1971.
  • Nieber, J. L., Modeling finger development and persistence in initially dry porous media, Geoderma, 70, 207229, 1996.
  • Nieber, J. L., The relation of preferential flow to water quality, and its theoretical and experimental quantification, in Preferential Flow, Water Movement and Chemical Transport in the Environment, edited by D. Bosch, and K. King, pp. 110, Am. Soc. of Agric. Eng., St. Joseph, Mich., 2000.
  • Nieber, J., A. Sheshukov, A. Egorov, and R. Dautov, Non-equilibrium model for gravity-driven fingering in water repellent soils: Formulation and 2-D simulations, in Soil Water Repellency: Occurrence, Consequences and Amelioration, edited by C. J. Ritsema, and L. W. Dekker, pp. 245257, Elsevier Sci., New York, 2003.
  • Otto, F., L1-contraction and uniqueness for quasilinear elliptic-parabolic equations, J. Differential Equations, 131, 2038, 1996.
  • Otto, F., L1-contraction and uniqueness for unstationary saturated-unsaturated water flow in porous media, Adv. Math. Sci. Appl., 7, 537553, 1997.
  • Panfilov, M., Upscaling two-phase flow in double porosity media: Nonuniform homogenization, in Recent Advances in Problems of Flow and Transport in Porous Media, edited by J. M. Crolet, and M. E. Hatri, pp. 195215, Kluwer Acad., Norwell, Mass., 1998.
  • Parlange, J.-Y., Theory of water-movement in soils: 2. One-dimensional infiltration, Soil Sci., 111, 170174, 1971.
  • Philip, J. R., The theory of infiltration, 4, Sorptivity analysis of algebraic infiltration equations, Soil Sci., 84, 257264, 1957.
  • Philip, J. R., Stability analysis of infiltration, Soil Sci. Soc. Am. Proc., 39, 10421049, 1975.
  • Prazak, J. M., M. Sir, F. Kubik, J. Tywoniak, and C. Zarcone, Oscillation phenonena in gravity-driven drainage in coarse porous media, Water Resour. Res., 28, 18491855, 1992.
  • Raats, P. A. C., Unstable wetting fronts in uniform and non-uniform soils, Soil Sci. Soc. Am. Proc., 37, 681685, 1973.
  • Reed, M., and B. Simon, Methods of modern mathematical physics. 4. Analysis of operators, Academic, New York, 1978.
  • Ritsema, C. J., L. W. Dekker, J. M. H. Hendrickx, and W. Hamminga, Preferential flow mechanism in a water repellent sandy soil, Water Resour. Res., 29, 21832193, 1993.
  • Roth, K., Steady state flow in an unsaturated, two-dimensional, macroscopically homogeneous, Miller-similar medium, Water Resour. Res., 31, 21272140, 1995.
  • Selker, J. S., J.-Y. Parlange, and T. Steenhuis, Fingered flow in two dimensions, 2, Predicting moisture profile, Water Resour. Res., 28, 25232528, 1992.
  • Shalit, G., T. S. Steenhuis, H. M. Hakvoort, J. Boll, L. D. Geohring, and H. M. Van-Es, Subsurface drainage water quality from structured soil, J. Irrig. Drain. Eng., 121, 239247, 1995.
  • Ursino, N., Linear stability analysis of infiltration, analytical and numerical solution, Transp. Porous Media, 38, 261271, 2000.