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Statistical description of the diffusion of a passive tracer in a random velocity field


A M Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Pyzhevskii per. 3, Moscow, 109017, Russian Federation

A single functional approach is used to treat the problem of the diffusion of a tracer in a random velocity field, posed in a general form. Approximate methods leading to various approximate solutions and the conditions of their validity are examined. Plane parallel average flow is considered in detail and some features of statistical solutions are discussed for the simplest case.

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Fulltext is also available at DOI: 10.1070/PU1994v037n05ABEH000110
PACS: 47.27.Qb, 92.10.Eq, 92.60.Ek (all)
DOI: 10.1070/PU1994v037n05ABEH000110
URL: https://ufn.ru/en/articles/1994/5/b/
A1994PG23700002
Citation: Klyatskin V I "Statistical description of the diffusion of a passive tracer in a random velocity field" Phys. Usp. 37 501–513 (1994)
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Оригинал: Кляцкин В И «Статистическое описание диффузии пассивной примеси в случайном поле скоростей» УФН 164 531–544 (1994); DOI: 10.3367/UFNr.0164.199405b.0531

References (32) ↓ Cited by (36) Similar articles (18)

  1. Batchelor G R J Fluid Mech. 5 113 (1959)
  2. Batchelor G R, Howells L D, Townsend A A J. Fluid Mech. 5 134 (1959)
  3. Roberts P H J. Fluid Mech. 11 257 (1961)
  4. Kraichnan R H Phys. Fluids 11 945 (1968)
  5. Kraichnan R H Phys. Fluids 13 22 (1970)
  6. Saffman P G Phys. Fluids 12 1786 (1969)
  7. McLaughlin D W, Papanicolaou G C, Pironneau O R SIAM J. Appl. Math. 45 780 (1985)
  8. Klyatskin V I Statisticheskoe Opisanie Dinamicheskikh Sistem S Fluktuiruyushchimi Parametrami (Statistical Description Of Dynamical Systems With Fluctuating Parameters) (Moscow: Nauka, 1975)
  9. Klyatskin V I Ondes Et Equations St Ochastiques Dans Les Milieux Aleatoirement Non Homogenes (Besancon Cedex: Les Editions de Physique, 1985)
  10. Klyatskin V I Stokhasticheskie Uravneniya I Volny V Sluchaino Neodnorodnoi Srede (Stochastic Equations And Waves In Randomly Inhomogeneous Media) (Moscow: Nauka, 1980)
  11. Monin A S, Yaglom A M Statisticheskaya Gidrodinamika Vol. Vol. 1 (Moscow: Nauka, 1965); Monin A S, Yaglom A M Statisticheskaya Gidrodinamika Vol. Vol. 2 (Moscow: Nauka, 1967); English translation, Monin A S, Yaglom A M Statistical Fluid Mechanics (Cambridge, MA: MIT Press, 1975)
  12. Furutsu K J. Res. Natl. Bur. Stand. D 667 303 (1963)
  13. Novikov E A Zh. Exp. Teor. FIZ. 47 1919 (1964); Novikov E A Sov. Phys. JETP 20 1290 (1965)
  14. Donsker M D Proceedings of the Conference on the Theory and Applications of Analysis in Functional Space (New York: MIT Press, 1964)
  15. Samokhin F F, Chechetkin V R Izv. Aka D. Nauk SSSR, Fiz. Atm Os. Okeana 27 621 (1991); Samokhin F F, Chechetkin V R Izv. Acad. Sci. USS R, Atm Os. Ocean. Phys. 27 434 (1991)
  16. Lutovinov V S, Chechetkin V R Izv. Ak Ad. Nauk SSS R, Fiz. Atm Os. Okeana 25 266 (1989); Lutovinov V S, Chechetkin V R Izv. Acad. Sci. USS R, Atm Os. Ocean. Phys. 27 195 (1989)
  17. Shapiro V E, Loginov V M Dinamicheskie Sistemy Pri Sluchainykh Vozdeistviyakh (Dynamical Systems Under Random Influences) (Novosibirsk: Nauka, 1983)
  18. Klyatskin V I, Tatarskii V I Izv. Vyssh. Uchebn. Zaved., Radiofiz. 14 1400 (1972)
  19. Careta A, Sagues F, Ramirez-Piscina L, Sancho J V J. St At. Phys. 71 235 (1993)
  20. Vainshtein S I, Ruzmaikin F F, Zel’dovich Ya B Turbulentnoe Dinamo V Astrofizike (Turbulent Dynamo In Astrophysics) (Moscow: Nauka, 1980)
  21. Lipscombe J T, Frenkel A L, ter Har D J. Stat. Phys. 63 305 (1991)
  22. Klyatskin V I Lect. Appl. Math. 27 447 (1991)
  23. Dolganskii F V, Klyatskin V I, Obukhov A M, Chusov M A Nelineinye Sistemy Gidrodinamicheskogo Tipa (Nonlinear Systems Of The Hydrodynamic Type) (Moscow: Nauka, 1974)
  24. Gledzer E V, Dolzhanskii F V, Obukhov A M Sistemy Gidrodina-micheskogo Tipa I Ikh Primeneniya (Systems Of The Hydrodynamic Type And Their Applications) (Moscow: Nauka, 1981)
  25. Csanady G T Turbulent Diffusion In The Environment (D ordrecht: Reidel, 1980)
  26. Zambianchi E, Griffa A Preprint (Miami, FL: Rosenstiel School of Marine and Atmospheric Science, University of Miami, 1993)
  27. Crisanti A, Vulpiani A J. Stat. Phys. 70 197 (1993)
  28. Saichev A I Dyn. Syst. 1 1 (1993)
  29. Klyatskin V I, Saichev A I Usp. Fiz. Nauk 162 161 (1992); Klyatskin V I, Saichev A I Sov. Phys. Usp. 35 231 (1992)
  30. Sinai Ya G, Yakhot V Phys. Rev. Lett. 63 1962 (1989)
  31. Chen H, Chen S, Kraichnan R H Phys. Rev. Lett. 63 265 (1989)
  32. Kimura Y, Kraichnan R H Phys. Fluids A 5 2264 (1993)

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