Effect of Evaporation or Infiltration on the Free Surface of Groundwater in Certain Problems of Underground Hydromechanics

E. N. Bereslavskii^1,

¹St. Petersburg State University for Civil Aviation, St. Petersburg, Russia

Cite this paper

E. N. Bereslavskii. Effect of Evaporation or Infiltration on the Free Surface of Groundwater in Certain Problems of Underground Hydromechanics. American Journal of Applied Mathematics and Statistics. 2017; 5(5):159-163. doi: 10.12691/AJAMS-5-5-1

Abstract

Within the framework of the theory of plane steady filtration of an incompressible fluid according to Darcy’s law, two limiting schemes modeling the filtration flows under the Joukowski tongue through a soil massive spread over an impermeable foundation or strongly permeable confined water bearing horizon are considered.

Keywords

filtration, infiltrations, evaporation, groundwater, free surface, tongue of Zhukovsky, Polubarinova-Cochina’s method, complex velocity, conformal mappings, Fuchsian equation

Copyright

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References

[1]	N. E. Joukowski, Infiltration of Water through Dams. Collected Works (Gostekhizdat, Moscow, 1950), Vol. 7, [in Russian].
[2]	P. Ya. Polubarinova_Kochina, Theory of Motion of Soil Waters (Gostekhizdat, Moscow, 1952; Nauka, Moscow, 1977) [in Russian].
[3]	Development of Investigations on the Theory of Filtration in the USSR (1917-1967), Ed. by P. Ya. Polubarinova Kochina (Nauka, Moscow, 1967) [in Russian].
[4]	P. Ya. Kochina, E. N. Bereslavskii, and N. N. Kochina, Analytical Theory of Linear Differential Equations of the Fuks Class and Certain Problems of Underground Hydromechanics. Preprint. No. 567 (In-t Problems of Mechanics of the RAS, Moscow, 1996), Part 1 [in Russian].
[5]	E. N. Bereslavskii and P. Ya. Kochina, Some equations of the Fuchs class in hydro and aerodynamics // Fluid Dynamics, 1992, v.27, i. 5, p. 603-607.
[6]	E. N. Bereslavskii and P. Ya. Kochina. Differential equations of the Fuchs class encountered in some problems of mechanics of liquids and gases // Fluid Dynamics, 1997, v. 32, i. 5, p. 619-625.
[7]	V. V. Golubev, Lectures on Analytical Theory of Differential Equations (Gostekhizdat, Moscow, 1950) [in Russian].
[8]	E. N. Bereslavskii. Spin fresh water salt water during filtration of the cold snap sprinkler // Journal of Applied Mathematics and Mechanics, 1989, v. 53, i. 3, p. 350-355.
[9]	E. N. Bereslavskii. The intake of purified fresh water with filtration from a reservoir // Journal of Applied Mathematics and Mechanics, 1990, v. 54, i. 5, p. 714-718.
[10]	E. N. Bereslavskii. A hydrodynamic model of the pressing out of stagnant salt waters by fresh waters for flow around a Zhukovski sheet pile // Report of the Academy of Sciences of the USSR, 1998, v. 363, i. 4, p. 479-482.
[11]	V. V. Vedernikov. K teorii drenazha // Report of the Academy of Sciences of the USSR, 1939, v. XXIII, i. 4, p. 335-337.
[12]	V. V. Vedernikov. K teorii drenazha // Report of the Academy of Sciences of the USSR, 1948, v. LIX, i. 6, p. 1069-1072.
[13]	V. V. Vedernikov, Filtracija pri nalichii drenirujushego ili vodonosnogo sloja // Report of the Academy of Sciences of the USSR, 1949, v. LXIX, i. 5, p. 619-622.
[14]	F. B. Nelson-Skornyakov. Pritekanie gruntovyh vod so svobodnoj poverhnost’ju k sisteme dren pri glubokom zaleganii vodoupora // Izv. AS USSR, OTN, 1941, i. 1, p. 126-128.
[15]	F. B. Nelson-Skornyakov. Dvizhenie gruntovoj vody so svobodnoj poverhnust’ju cherez plotinu s dvumja diafragmami // Izv. AS USSR, 1941, OTN, i. 3, p. 39-44.