| Автор | Waechter, R. T. |
| Автор | Philip, J. R. |
| Дата выпуска | 1985 |
| dc.description | An exact analog exists between steady quasi‐linear flow in unsaturated soils and porous media and the scattering of plane pulses, and the analog carries over to the scattering of plane harmonic waves. Numerous established results, and powerful techniques such as the Watson transform, are thus available for the solution and understanding of problems of unsaturated flow. These are needed, in particular, to provide the asymptotics of the physically interesting and practically important limit of flows strongly dominated by gravity, with capillary effects weak but nonzero. This is the limit of large s, with s a characteristic length of the water supply surface normalized with respect to the sorptive length of the soil. These problems are singular in the sense that ignoring capillarity gives a totally incorrect picture of the wetted region. In terms of the optical analog, neglecting capillarity is equivalent to using geometrical optics, with coherent shadows projected to infinity. The paper deals specifically with steady infiltration from circular cylindrical and spherical cavities. The asymptotic methods prove remarkably accurate, even far from the limit. The results replace, and explain, previous semiempirical estimates of the limiting behavior. One notable result is that the depth of the penumbra (effectively wetted region) for the cylinder is 128 times the depth for the sphere, confirming and supplementing previous studies. An odd byproduct is that we correct a long‐standing classical result in scattering theory. The scope for extending these methods to flows in other geometries, to heterogeneous soils, and generally to linear convection‐diffusion processes, is indicated briefly. |
| Формат | application.pdf |
| Копирайт | Copyright 1985 by the American Geophysical Union. |
| Тема | HYDROLOGY |
| Тема | Hydrologic scaling |
| Тема | Irrigation |
| Тема | Soil moisture |
| Тема | Instruments and techniques: modeling |
| Название | Steady Two‐ and Three‐Dimensional Flows in Unsaturated Soil: The Scattering Analog |
| Тип | article |
| DOI | 10.1029/WR021i012p01875 |
| Electronic ISSN | 1944-7973 |
| Print ISSN | 0043-1397 |
| Журнал | Water Resources Research |
| Том | 21 |
| Первая страница | 1875 |
| Последняя страница | 1887 |
| Выпуск | 12 |
| Библиографическая ссылка | Batu, V., Steady infiltration from single and periodic strip sources, Soil Sci. Soc. Am. J., 42, 544–559, 1978. |
| Библиографическая ссылка | Beckman, P., W.Franz, Berechnung der Streuquenschnitte von Kugel und Zylinder unter Anwendung einer modifizierten Watson‐Transformation, Z. Naturforsch., 12a, 533–537, 1957. |
| Библиографическая ссылка | Bowman, J. J., T. B. A.Senior, P. L. E.Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes, North‐Holland, Amsterdam, 1969. |
| Библиографическая ссылка | Carslaw, H. S., J. C.Jaeger, Conduction of Heat in Solids2, Clarendon Press, Oxford, 1959. |
| Библиографическая ссылка | Fock, V. A., Electromagnetic Diffraction and Propagation Problems, Pergamon, New York, 1965. |
| Библиографическая ссылка | Jones, D. S., Approximate methods in high‐frequency scattering, Proc. R. Soc. London, Ser. A, 239, 338–348, 1957. |
| Библиографическая ссылка | Keller, J. B., A geometrical theory of diffraction, Calculus of Variations and its ApplicationsL. M.Graves, 27–52, American Mathematical Society, Providence, R. I., 1958. |
| Библиографическая ссылка | Keller, J. B., Geometrical theory of diffraction, J. Opt. Soc. Am., 52, 116–130, 1962. |
| Библиографическая ссылка | Keller, J. B., Rays, waves and asymptotics, Bull. Am. Math. Soc., 84, 727–750, 1978. |
| Библиографическая ссылка | Keller, J. B., Progress and prospects in the theory of linear wave propagation, SIAM Rev., 21, 229–245, 1979. |
| Библиографическая ссылка | Kirchhoff, G., Vorlesungen über der Theorie der Wärme, Barth, Leipzig, 1894. |
| Библиографическая ссылка | Masters, J. I., Some applications in physics of the P function, J. Chem. Phys., 23, 1865–1874, 1955. |
| Библиографическая ссылка | Olver, F. J. W., Bessel functions of integer order, Handbook of Mathematical FunctionsM.Abramowitz, I. A.Stegun, 355–433, U.S. Government Printing Office, Washington, D. C., 1964. |
| Библиографическая ссылка | Philip, J. R., The theory of infiltration, 1, The infiltration equation and its solution, Soil Sci., 83, 345–357, 1957. |
| Библиографическая ссылка | Philip, J. R., Absorption and infiltration in two‐ and three‐dimensional systems, Water in the Unsaturated Zone, 1R. E.Rijtema, H.Wassink, 503–525, UNESCO, Paris, 1966. |
| Библиографическая ссылка | Philip, J. R., Steady infiltration from buried point sources and spherical cavities, Water Resour. Res., 4, 1039–1047, 1968. |
| Библиографическая ссылка | Philip, J. R., Theory of infiltration, Adv. Hydrosci., 5, 215–296, 1969. |
| Библиографическая ссылка | Philip, J. R., General theorem on steady infiltration from surface sources, with application to point and line sources, Soil Sci. Soc. Am. Proc., 35, 867–871, 1971. |
| Библиографическая ссылка | Philip, J. R., Steady infiltration from buried, surface, and perched point and line sources in heterogeneous soils, I, Analysis, Soil Sci. Soc. Am. Proc., 36, 268–273, 1972. |
| Библиографическая ссылка | Philip, J. R., Recent progress in the solution of nonlinear diffusion equations, Soil Sci., 117, 257–264, 1974. |
| Библиографическая ссылка | Philip, J. R., Infiltration in one, two, and three dimensions, Advances in Infiltration, 1–13, American Society of Agricultural Engineers, St. Joseph, Mich., 1983. |
| Библиографическая ссылка | Philip, J. R., Aspects of quasilinear infiltration from surface sources, especially the case α = 0, Water Resour. Res., 20, 633–635, 1984a. |
| Библиографическая ссылка | Philip, J. R., Mathematics, soil, and water, New Zealand Math. Soc. Newslett., 31, 28–35, 1984b. |
| Библиографическая ссылка | Philip, J. R., Steady infiltration from circular cylindrical cavities, Soil Sci. Soc. Am. J., 48, 270–278, 1984c. |
| Библиографическая ссылка | Philip, J. R., Steady infiltration from spherical cavities, Soil Sci. Soc. Am. J., 48, 740–749, 1984d. |
| Библиографическая ссылка | Philip, J. R., Reply to “Comments on ‘Steady infiltration from spherical cavities'”, Soil Sci. Soc. Am. J., 49, 788–789, 1985a. |
| Библиографическая ссылка | Philip, J. R., Approximate analysis of the borehole permeameter in unsaturated soil, Water Resour. Res., 21, 1025–1034, 1985b. |
| Библиографическая ссылка | Philip, J. R., R. I.Forrester, Steady infiltration from buried, surface, and perched point and line sources in heterogeneous soils, II, Flow details and discussion, Soil Sci. Soc. Am. Proc., 39, 408–414, 1975. |
| Библиографическая ссылка | Raats, P. A. C., Steady infiltration from point sources, cavities, and basins, Soil Sci. Soc. Am. Proc., 35, 689–694, 1971. |
| Библиографическая ссылка | Rubinow, S., T. T.Wu, First correction to the geometrical‐optics scattering cross section from cylinders and spheres, J. Appl. Phys., 27, 1032–1039, 1956. |
| Библиографическая ссылка | Waechter, R. T., Steady longitudinal motion of an insulating cylinder in a conducting fluid, Proc. Camb. Philos. Soc., 64, 1165–1201, 1968. |
| Библиографическая ссылка | Waechter, R. T., Steady rotation of a body of revolution in a conducting fluid, Proc. Camb. Philos. Soc., 65, 329–350, 1969. |
| Библиографическая ссылка | Watson, G. N., The transmission of electric waves around the earth, Proc. R. Soc. London, Ser. A, 95, 546–563, 1918. |
| Библиографическая ссылка | Watson, G. N., A Treatise on the Theory of Bessel Functions2, Cambridge University Press, New York, 1944. |
| Библиографическая ссылка | Wu, T. T., High‐frequency scattering, Phys. Rev., 104, 1201–1212, 1956. |
