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Reconstruction of streamline topology, and percolation models of turbulent transport


Institute of Tokamak Physics, National Research Centre ‘Kurchatov Institute’, pl. akad. Kurchatova 1, Moscow, 123182, Russian Federation

This paper discusses in detail the percolation models of turbulent diffusion that help to establish nontrivial relationships between theoretical concepts used in turbulence, dynamical systems, transport, etc. theories. This approach is particularly important due to the need to describe turbulence in the presence of coherent structures, streamline reconstructions, and drift and dissipation effects. In such regimes the conventional quasilinear description is inconsistent with experimental results, necessitating the search for fundamentally new models and approaches. Most attention is given to the scaling concept, an important and widely used tool among theoreticians and experimentalists.

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Fulltext is also available at DOI: 10.3367/UFNe.0183.201303b.0257
PACS: 05.40.−a, 47.27.T−, 47.53.+n (all)
DOI: 10.3367/UFNe.0183.201303b.0257
URL: https://ufn.ru/en/articles/2013/3/b/
000320226200002
2013PhyU...56..243B
Citation: Bakunin O G "Reconstruction of streamline topology, and percolation models of turbulent transport" Phys. Usp. 56 243–260 (2013)
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Received: 2nd, February 2012, revised: 27th, May 2012, 2nd, June 2012

Îðèãèíàë: Áàêóíèí Î Ã «Ïåðåñòðîéêà òîïîëîãèè ëèíèé òîêà è ïåðêîëÿöèîííûå ìîäåëè òóðáóëåíòíîãî ïåðåíîñà» ÓÔÍ 183 257–276 (2013); DOI: 10.3367/UFNr.0183.201303b.0257

References (75) ↓ Cited by (5) Similar articles (20)

  1. Monin A S, Yaglom A M Statisticheskaya Gidromekhanika Vol. 1, 2 (M.: Nauka, 1965, 1967); Monin A S, Yaglom A M Statistical Fluid Mechanics Vol. 1, 2 (Cambridge, Mass.: MIT Press, 1971, 1975)
  2. Barenblatt G I Podobie, Avtomodel’nost’, Promezhutochnaya Asimptotika (L.: Gidrometeoizdat, 1982); Barenblatt G I Scaling, Self-Similarity, And Intermediate Asymptotics (Cambridge: Cambridge Univ. Press, 1996)
  3. Frisch U Turbulence: The Legacy Of A N Kolmogorov (Cambridge: Cambridge Univ. Press, 1995); Frish U Turbulentnost’. Nasledie A.N. Kolmogorova (M.: FAZIS, 1998)
  4. Klyatskin V I Usp. Fiz. Nauk 178 419 (2008); Klyatskin V I Phys. Usp. 51 395 (2008)
  5. Golitsyn G S Issledovanie Konvektsii s Geofizicheskimi Prilozheniyami i Analogiyami (L.: Gidrometeoizdat, 1980)
  6. Lebedev V V Fluktuatsionnye Effekty v Makrofizike (M.: MTsNMO, 2004)
  7. Childress S, Gilbert A D Stretch, Twist, Fold: The Fast Dynamo (Berlin: Springer, 1995)
  8. Zel’dovich Ya B, Ruzmaikin A A, Sokoloff D D Magnetic Fields In Astrophysics (New York: Gordon and Breach, 1983); Zel’dovich Ya B, Ruzmaikin A A, Sokolov D D Magnitnye Polya v Astrofizike (Moskva - Izhevsk: RKhD, Inst. komp’yut. issled., 2006)
  9. Bakunin O G Turbulence And Diffusion. Scaling Versus Equations (New York: Springer, 2008)
  10. Sornette D Critical Phenomena In Natural Sciences (Berlin: Springer, 2006)
  11. Zelenyi L M, Veselovskii I S (Red.) Plazmennaya Geliogeofizika Vol. 1, 2 (M.: Fizmatlit, 2008)
  12. Bakunin O G Chaotic Flows. Correlation Effects, Transport, And Structures (Berlin: Springer-Verlag, 2011)
  13. Klyatskin V I Stokhasticheskie Uravneniya Glazami Fizika (M.: Fizmatlit, 2001)
  14. Uchaikin V V Usp. Fiz. Nauk 173 847 (2003); Uchaikin V V Phys. Usp. 46 821 (2003)
  15. Wiggins S Chaotic Transport In Dynamical Systems (New York: Springer-Verlag, 1991)
  16. Kolmogorov A N Dokl. Akad. Nauk SSSR 30 299 (1941); Kolmogoroff A N C.R. (Dokl.) Acad. Sci. USSR 30 301 (1941)
  17. Obukhov A M Dokl. Akad. Nauk SSSR 32 19 (1941); Obukhov A M C.R. (Dokl.) Acad. Sci. USSR 32 22 (1941)
  18. Kuznetsov E A, Ruban V P Zh. Eksp. Teor. Fiz. 118 893 (2000); Kuznetsov E A, Ruban V P JETP 91 775 (2000)
  19. Budaev V P, Savin S P, Zelenyi L M Usp. Fiz. Nauk 181 905 (2011); Budaev V P, Savin S P, Zelenyi L M Phys. Usp. 54 875 (2011)
  20. Bakunin O G Usp. Fiz. Nauk 173 317 (2003); Bakunin O G Phys. Usp. 46 309 (2003)
  21. Balescu R Aspects Of Anomalous Transport In Plasmas (Bristol: IOP Publ., 2005)
  22. Kadomtsev B B, Pogutse O P Plasma Physics and Controlled Nuclear Fusion Research 1978. Proc. of the 7th Intern. Conf., IAEA, Innsbruck, Austria, August 23 - 30, 1978 Vol. 1 (Vienna: Intern. Atomic Energy Agency, 1978) p. 649
  23. Zel’dovich Ya B Pis’ma ZhETF 38 51 (1983); Zel’dovich Ya B JETP Lett. 38 57 (1983)
  24. Galeev A A, Kuznetsova M M, Zeleny L M Space Sci. Rev. 44 1 (1986)
  25. Isichenko M B Rev. Mod. Phys. 64 961 (1992)
  26. Bakunin O G Usp. Fiz. Nauk 173 757 (2003); Bakunin O G Phys. Usp. 46 733 (2003)
  27. Zelenyi L M, Milovanov A V Usp. Fiz. Nauk 174 809 (2004); Zelenyi L M, Milovanov A V Phys. Usp. 47 749 (2004)
  28. Taylor G I Proc. London Math. Soc. 2 20 196 (1921)
  29. Vedenov A A, Velikhov E P, Sagdeev R Z Nucl. Fusion 1 82 (1961)
  30. Richardson L F Proc. R. Soc. Lond. A 110 709 (1926)
  31. Batchelor G K Quart. J. R. Meteorolog. Soc. 76 133 (1950)
  32. Zel’dovich Ya B Zh. Eksp. Teor. Fiz. 7 1466 (1937)
  33. Isichenko M B i dr. Zh. Eksp. Teor. Fiz. 96 913 (1989); Isichenko M B et al. Sov. Phys. JETP 69 517 (1989)
  34. Saleur H, Duplantier B Phys. Rev. Lett. 58 2325 (1987)
  35. Sokolov I M Usp. Fiz. Nauk 150 221 (1986); Sokolov I M Sov. Phys. Usp. 29 924 (1986)
  36. Levinshtein M E, Shchur M S, Efros A L Zh. Eksp. Teor. Fiz. 69 2203 (1975); Levinshtein M E, Shur M S, Éfros A L Sov. Phys. JETP 42 1120 (1976)
  37. Osipenko M V, Pogutse O P, Chudin N V Fizika Plazmy 13 953 (1987); Osipenko M V, Pogutse O P, Chudin N V Sov. J. Plasma Phys. 13 550 (1987)
  38. Kleva R G, Drake J F Phys. Fluids 27 1686 (1984)
  39. Stauffer D Introduction To Percolation Theory (London: Taylor and Francis, 1985)
  40. Fannjiang A, Papanicolaou G J. Stat. Phys. 88 1033 (1997)
  41. Avellaneda M, Elliott F (Jr.), Apelian C J. Stat. Phys. 72 1227 (1993)
  42. Gruzinov A V, Isichenko M B, Kalda Ya L Zh. Eksp. Teor. Fiz. 97 476 (1990); Gruzinov A V, Isichenko M B, Kalda Ya L Sov. Phys. JETP 70 263 (1990)
  43. Isichenko M B, Kalda J J. Nonlin. Sci. 1 255 (1991)
  44. Isichenko M B, Kalda J J. Nonlin. Sci. 1 375 (1991)
  45. Bakunin O G Chaos Solitons Fractals 23 1703 (2005)
  46. Misguich J H et al. Physicalia Mag. 20 103 (1998)
  47. Zimbardo G, Veltri P, Pommois P Phys. Rev. E 61 1940 (2000)
  48. Trugman S A Phys. Rev. B 27 7539 (1983)
  49. Yushmanov P N, Oliakov A N Comm. Plasma Phys. Control. Fusion 14 313 (1992)
  50. Bakunin O G Plasma Phys. Control. Fusion 45 1909 (2003)
  51. Bakunin O G Rep. Prog. Phys. 67 965 (2004)
  52. Horton W Rev. Mod. Phys. 71 735 (1999)
  53. Terry P W Rev. Mod. Phys. 72 109 (2000)
  54. Bakunin O G J. Plasma Phys. 71 435 (2005)
  55. Bakunin O G Physica A 347 289 (2005)
  56. Bakunin O G Review Of Plasma Physics Vol. 24 (Ed. V D Shafranov) (Berlin: Springer-Verlag, 2008) p. 53
  57. Zaslavsky G M Physics Of Chaos In Hamiltonian Systems (River Edge, N.J.: Imperial College Press, 1998); Zaslavskii G M Fizika Khaosa v Gamil’tonovykh Sistemakh (Moskva - Izhevsk: Inst. komp’yut. issled., 2004)
  58. Bohr T et al. Dynamical Systems Approach To Turbulence (Cambridge: Cambridge Univ. Press, 2005)
  59. Zaslavsky G M Phys. Rep. 371 461 (2002)
  60. Vainshtein S I , Zel’dovich Ya B, Ruzmaikin A A Turbulentnoe Dinamo v Astrofizike (M.: Nauka, 1980)
  61. Pope S B Turbulent Flows (Cambridge: Cambridge Univ. Press, 2000)
  62. Biskamp D Magnetohydrodynamic Turbulence (Cambridge: Cambridge Univ. Press, 2003)
  63. Bakunin O G Physica A 345 1 (2005)
  64. Nieuwstadt F T M, van Dop H (Eds) Atmospheric Turbulence And Air Pollution Modelling (Dordrecht: D. Reidel, 1982)
  65. Arnold V I, Khesin B A Topological Methods In Hydrodynamics (New York: Springer, 1998); Arnol’d V I, Khesin B A Topologicheskie Metody v Gidrodinamike (M.: Izd-vo MTsNMO, 2007)
  66. Moffatt H K et al. (Ed.) Topological Aspects Of The Dynamics Of Fluids And Plasmas (NATO ASI Series, E) Vol. 218 (Dordrecht: Kluwer Acad. Publ., 1992)
  67. Bakunin O G Plasma Phys. Control. Fusion 47 1857 (2005)
  68. Zimbardo G et al. Phys. Plasmas 2 2653 (1995)
  69. Batchelor G K Phys. Fluids 12 II-233 (1969)
  70. Wesson J Tokamaks (Oxford: Clarendon Press, 1987)
  71. Vainshtein S I Magnitnye Polya v Kosmose (M.: Nauka, 1983)
  72. Bakunin O G J. Plasma Phys. 72 647 (2006)
  73. Bakunin O G, Schep T J Phys. Lett. A 322 105 (2004)
  74. West B J, Bologna M, Grigolini P Physics Of Fractal Operators (New York: Springer, 2003)
  75. Bakunin O G Physica A 351 241 (2005)
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