Issues

 / 

2011

 / 

September

  

Reviews of topical problems


Investigation of intermittency and generalized self-similarity of turbulent boundary layers in laboratory and magnetospheric plasmas: towards a quantitative definition of plasma transport features

 a, b,  b,  b
a National Research Centre ‘Kurchatov Institute’, pl. Akademika Kurchatova 1, Moscow, 123182, Russian Federation
b Space Research Institute, Russian Academy of Sciences, Profsoyuznaya str. 84/32, Moscow, 117997, Russian Federation

A comparative analysis of the fundamental properties of fluctuations in the vicinity of boundaries in fusion plasmas and in plasmas of magnetospheric turbulent boundary layers (TBLs) shows the similarity of their basic statistical characteristics, including the scaling of the structure functions and mutifractal parameters. Important features observed include intermittent fluctuations and anomalous mass and momentum transport, due to sporadic plasma flow injections with large flow amplitudes occuring with a much higher probability than predicted for classical Gaussian diffusion. Turbulence in edge fusion plasmas and in TBLs exhibits general self-similarity in a wide range of scales extending to the dissipation scale. Experimental scalings obtained for plasma TBLs are compared with neutral fluid results, revealing the universal properties of developed turbulence. TBL scalings are described within the log-Poisson model, which takes quasi-one-dimensional dissipative structures into account. The time ($\tau$) dependence of the mean-square displacement $\langle \delta x^2 \rangle$ obtained from the experimental parameters of the log-Poisson distribution takes the form $\langle \delta x^2 \rangle \propto \tau^{\alpha}$ with $\alpha \approx$ 1.2–1.8 and indicates the presence of superdiffusion in the TBLs studied. Determining the nature of the generalized diffusion process from available regular data is a necessary step toward the quantitative description of TBL transport.

Fulltext pdf (1.4 MB)
Fulltext is also available at DOI: 10.3367/UFNe.0181.201109a.0905
PACS: 05.45.−a, 47.27.−i, 52.35.Ra (all)
DOI: 10.3367/UFNe.0181.201109a.0905
URL: https://ufn.ru/en/articles/2011/9/a/
000298416500001
2011PhyU...54..875B
Citation: Budaev V P, Savin S P, Zelenyi L M "Investigation of intermittency and generalized self-similarity of turbulent boundary layers in laboratory and magnetospheric plasmas: towards a quantitative definition of plasma transport features" Phys. Usp. 54 875–918 (2011)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 2nd, July 2010, revised: 22nd, February 2011, 2nd, March 2011

Оригинал: Будаев В П, Савин С П, Зелёный Л М «Наблюдения перемежаемости и обобщённого самоподобия в турбулентных пограничных слоях лабораторной и магнитосферной плазмы: на пути к определению количественных характеристик переноса» УФН 181 905–952 (2011); DOI: 10.3367/UFNr.0181.201109a.0905

References (300) ↓ Cited by (66) Similar articles (20)

  1. ’F’?’?’?’?’?’?р’?’? ’B ’v Dokl. Akad. Nauk SSSR 30 299 (1941); Kolmogorov A N C.R. (Dokl.) Acad. Sci. USSR 30 299 (1941)
  2. ’F’?’?’?’?’?’?р’?’? ’B ’v Dokl. Akad. Nauk SSSR 32 19 (1941); Kolmogorov A N C.R. (Dokl.) Acad. Sci. USSR 32 19 (1941)
  3. ’a’?’?’?’? A ’l, Ya’?’?’?’? ’B ’a ’lт’?т’?ст’?ch’?с’?’?ya ’?’?’?р’?’?’?kh’?’?’?’?’? (’a.: ’v’?у’?’?, 1965, 1967); Monin A S, Yaglom A M Statistical Fluid Mechanics Vol. 1, 2 (Cambridge, Mass.: MIT Press, 1971, 1975)
  4. Lathrop D P, Fineberg J, Swinney H L Phys. Rev. Lett. 68 1515 (1992)
  5. Cadot O et al. Phys. Rev. E 56 427 (1997)
  6. ’’’?’?’?’?у ’’ ’K, ’’’?фsh’?ts ’M ’a ’I’?’?р’?’?’?’?’?’?’?’?’? (’a.: ’v’?у’?’?, 1986); Landau L D, Lifshitz E M Fluid Mechanics (Oxford: Pergamon Press, 1987)
  7. Sreenivasan K R Frontiers In Experimental Fluid Mechanics (Ed. M Gad-el-Hak) (Berlin: Springer-Verlag, 1989) p. 159
  8. ’G’?р’?’?’?’?’?тт ’I ’R Usp. Mat. Nauk 59 (1) 45 (2004); Barenblatt G I Russ. Math. Surv. 59 47 (2004)
  9. Barenblatt G I, Prostokishin V M J. Fluid Mech. 248 521 (1993)
  10. Zagarola M V, Perry A E, Smits A J Phys. Fluids 9 2094 (1997)
  11. Barenblatt G I, Chorin A J Phys. Fluids 10 1043 (1998)
  12. ’F’?’?’?’?ts’?’? ’G ’G ’E’?’?р’?сы т’?’?р’?’? ’?’?’?’?’?ы Т. 4 (’z’?’? р’?’?. ’a ’B ’’’?’?’?т’?’?’?ch’?) (’a.: ’Bт’?’?’?’?’?’?т, 1964) с. 188; Kadomtsev B B Reviews In Plasma Physics Vol. 4 (Ed. M A Leontovich) (New York: Consultants Bureau, 1971)
  13. ’F’?’?’?’?ts’?’? ’G ’G ’F’?’?’?’?’?т’?’?’?ы’? ya’?’?’?’?’?ya ’? ’?’?’?’?’?’? (’a.: ’v’?у’?’?, 1988); Kadomtsev B B Reviews Of Plasma Physics Vol. 22 (Ed. V D Shafranov) (New York: Kluwer Acad./Plenum Publ., 2001) p. 1
  14. Zweben S J et al. Plasma Phys. Control. Fusion 49 S1 (2007)
  15. Carreras B A, Lynch V E, LaBombard B Phys. Plasmas 8 3702 (2001)
  16. Kadomtsev B B Tokamak Plasma: A Complex Physical System (Bristol: IOP Publ., 1992)
  17. ’l’?’?’?’? ’l ’z ’? ’?р. ’z’?сь’?’? Zh’e’n’s 74 620 (2001); Savin S P et al. JETP Lett. 74 547 (2001)
  18. Savin S et al. Nonlin. Proces. Geophys. 9 443 (2002)
  19. Savin S et al. Surv. Geophys. 26 95 (2005)
  20. Savin S et al. ’z’?сь’?’? Zh’e’n’s 87 691 (2008); Savin S et al. JETP Lett. 87 593 (2008)
  21. ’l’?’?’?’? ’l ’z ’? ’?р. ’z’?сь’?’? Zh’e’n’s 79 452 (2004); Savin S P et al. JETP Lett. 79 368 (2004)
  22. Savin S et al. Planet. Space Sci. 53 133 (2005)
  23. ’v’?’?’?’?’?’? ’M ’B, ’lтyu’?рт ’i ’p ’R’?’?. ’B’v ’l’l’l’i C’?р. ’I’?’?ф’?’?. (3) 408 (1964)
  24. Frisch U Turbulence. The Legacy Of A.N. Kolmogorov (Cambridge: Cambridge Univ. Press, 1995); ’sр’?sh ’p ’nур’?у’?’?’?т’?’?сть: ’v’?с’?’?’?’?’? ’B.’v. ’F’?’?’?’?’?’?р’?’?’? (’a.: ’s’?’?’?с, 1998)
  25. Budaev V P et al. Nucl. Fusion 48 024014 (2008)
  26. Scott B D Phys. Plasmas 12 062314 (2005)
  27. ’z’?стуkh’?’? ’E ’z Fiz. Plazmy 31 628 (2005); Pastukhov V P Plasma Phys. Rep. 31 577 (2005)
  28. ’O’?’?’?’?ы’? ’’ ’a, ’a’?’?’?’?’?’?’?’? ’B ’E Usp. Fiz. Nauk 174 809 (2004); Zelenyi L M, Milovanov A V Phys. Usp. 47 749 (2004)
  29. ’O’?’?’?’?ы’? ’’ ’a, ’E’?с’?’?’?’?с’?’?’? ’R ’l (’i’?’?.) ’z’?’?’?’?’?’?’?’?ya ’?’?’?’?’?’?’?’?ф’?’?’?’?’? (’a.: ’s’?’?’?’?т’?’?т, 2008)
  30. Biskamp D, Schwarz E Phys. Plasmas 8 3282 (2001)
  31. Biskamp D, Müller W-C Phys. Plasmas 7 4889 (2000)
  32. ’sр’?’? ’z ’I ’nур’?у’?’?’?т’?’?сть: ’?’?’?kh’?’?ы ’? ’?’?’?’?’?’? (’a. - ’Rzh’?’?с’?: ’R’?ст. ’?’?’?’?ьyuт. ’?сс’?’?’?., 2003)
  33. ’’’?’?’?’?у ’’ ’K, ’’’?фsh’?ts ’M ’a ’n’?’?р’?ya ’?’?’?ya (’a.: ’s’?’?’?’?т’?’?т, 2001); Landau L D, Lifshitz E M The Classical Theory Of Fields (Oxford: Pergamon Press, 1980)
  34. Prigogine I Introduction To Thermodynamics Of Irreversible Processes (Springfield, Ill.: Thomas, 1955); ’zр’?’?’?zh’?’? ’R ’E’?’?’?’?’?’?’? ’? т’?р’?’?’?’?’?’?’?’?’?у ’?’?’?’?р’?т’?’?ыkh ’?р’?ts’?сс’?’? (’a. - ’Rzh’?’?с’?: ’iKh’K, 2001)
  35. Parisi G, Frish U Turbulence And Predictability In Geophysical Fluid Dynamics And Climate Dynamics (Eds M Ghil, R Benzi, G Parisi) (Amsterdam: North-Holland, 1985) p. 71
  36. Gogoberidze G Phys. Plasmas 14 022304 (2007)
  37. ’a’?’?’?’?’?’?shch’?’?’?’? ’a ’K Dokl. Akad. Nauk SSSR 32 611 (1941); Milliontchikov M D C.R. (Dokl.) Acad. Sci. USSR 32 611 (1941)
  38. Kraichnan R H J. Fluid Mech. 5 497 (1959)
  39. Kadomtsev B B Plasma Turbulence (London: Academic Press, 1965)
  40. ’Gы’?’?’? ’B ’a, ’n’?’?ты’?’?’? ’R ’v Usp. Fiz. Nauk 163 (11) 19 (1993); Bykov A M, Toptygin I N Phys. Usp. 36 1020 (1993)
  41. ’Gр’?’?’?’?с’?’?’? ’l ’R ’E’?’?р’?сы т’?’?р’?’? ’?’?’?’?’?ы Т. 1 (’z’?’? р’?’?. ’a ’B ’’’?’?’?т’?’?’?ch’?) (’a.: ’I’?с’?т’?’?’?’?’?’?т, 1963) с. 183; Braginskii S I Reviews In Plasma Physics Vol. 1 (Ed. M A Leontovich) (New York: Consultants Bureau, 1965) p. 205
  42. Zeiler A, Drake J F, Rogers B Phys. Plasmas 4 2134 (1997)
  43. Horton W Phys. Rep. 192 1 (1990)
  44. Scott B Plasma Phys. Control. Fusion 39 471 (1997)
  45. Shуры’?’?’? ’i ’E Fiz. Plazmy 30 387 (2004); Shurygin R V Plasma Phys. Rep. 30 353 (2004)
  46. ’d’?сya’?’?’?’?’?’? ’’ ’E ’Iру’?’?’?’?ы’? с’?’?’?ст’?’? ’?’?фф’?р’?’?ts’?’?’?ь’?ыkh ур’?’?’?’?’?’?’? (’v’?’?’?с’?’?’?рс’?: ’R’?’?-’?’? ’l’d ’B’v ’l’l’l’i, 1962)
  47. Olver P J Applications Of Lie Groups To Differential Equations (New York: Springer-Verlag, 1993)
  48. Gusyatnikova V N et al. Acta Appl. Math. 15 23 (1989)
  49. ’l’?’?’?kh’?’? ’B ’E Dokl. Akad. Nauk SSSR 285 1101 (1985); Samokhin A V Sov. Phys. Dokl. 30 1020 (1985)
  50. ’Iр’?’?’?’?’? ’R ’z Priklad. Mekh. Tekh. Fiz. 9 (6) 103 (1968); Gridnev I P J. Appl. Mech. Tech. Phys. 9 718 (1968)
  51. Ibragimov N H (Ed.) CRC Handbook Of Lie Group Analysis Of Differential Equations Vol. 1 - 3 (Boca Raton: CRC Press, 1994 - 1996)
  52. Nucci M C Atti Semin. Mat. Fis. Univ. Modena 33 21 (1984)
  53. Biferale L, Procaccia I Phys. Rep. 414 43 (2005)
  54. Cartes C et al. Fluid Dyn. Res. 41 011404 (2009)
  55. Kolmogorov A N J. Fluid Mech. 13 82 (1962)
  56. ’zуkh’?’?ch’?’? ’E ’E ’pс’?. ’?’?kh’?’?’?’?’? 4 (1) 1 (2006)
  57. ’Bkh’?’?’?’?р ’B ’R, ’G’?р’?ст’?ts’?’?’? ’E ’G ’F’?’?’?т’?’?’?ya э’?’?’?тр’?’?’?’?’?’?’?’?’? (’a.: ’v’?у’?’?, 1981); Akhiezer A I, Berestetskii V B Quantum Electrodynamics (New York: Interscience Publ., 1965)
  58. ’B’?zh’?’?ya’? ’’ Ts, ’B’?т’?’?’?’? ’v ’E, ’E’?с’?’?ь’?’? ’B ’v Usp. Fiz. Nauk 166 1257 (1996); Adzhemyan L Ts, Antonov N V, Vasil’ev A N Phys. Usp. 39 1193 (1996)
  59. Chу’?’?’?р ’F ’E Zh. Eksp. Teor. Fiz. 108 1875 (1995); Chukbar K V JETP 81 1025 (1995)
  60. Chechkin A V, Gorenflo R, Sokolov I M Phys. Rev. E 66 046129 (2002)
  61. ’pch’?’?’?’?’? ’E ’E ’a’?т’?’? ’?р’?’?’?ыkh ’?р’?’?’?’?’?’?’?ыkh (’p’?ьya’?’?’?с’?: ’Bрт’?sh’?’?, 2008)
  62. ’’ya’?у’?’?’? ’B ’a ’d’?shch’?ya ’?’?’?’?ch’? ’?’? уст’?’?ch’?’?’?ст’? ’?’?’?zh’?’?’?ya (Kh’?рь’?’?’?: Kh’?рь’?’?’?с’?. ’?’?т’?’?. ’?’?shch-’?’?, 1892); ’’ya’?у’?’?’? ’B ’a ’d’?shch’?ya ’?’?’?’?ch’? ’?’? уст’?’?ch’?’?’?ст’? ’?’?’?zh’?’?’?ya (’a. - ’’.: ’I’R’n’n’’, 1950); ’z’?р’?’?’?’? ’?’? фр. ya’?., Liapounoff A "Problème général de la stabilité du mouvement" Ann. Fac. Sci. Toulouse 9 203 (1907); Liapounoff A Annals Of Mathematics Studies Vol. 17 (Princeton, N.J.: Princeton Univ. Press, 1947); ’?’?р’?’?’?’? ’?’? ’?’?’?’?. ya’?., Lyapunov A M The General Problem Of The Stability Of Motion (London: Taylor & Francis, 1992)
  63. ’dс’?’?’?’?’?ts ’E ’R ’nр. ’a’?с’?’?’?с’?’?’?’? ’?’?т. ’?’?shch-’?’? 19 179 (1968); Oseledets V I Trans. Moscow Math. Soc. 19 197 (1968)
  64. ’O’?с’?’?’?с’?’?’? ’I ’a, ’l’?’?’?’?’?’? ’i ’O ’E’?’?’?’?’?’?’? ’? ’?’?’?’?’?’?’?’?уyu ф’?’?’?’?у. ’dт ’?’?yaт’?’?’?’? ’?’? тур’?у’?’?’?т’?’?ст’? ’? kh’?’?с’? (’a.: ’v’?у’?’?, 1988); Sagdeev R Z, Usikov D A, Zaslavsky G M Nonlinear Physics: From The Pendulum To Turbulence And Chaos (Chur: Harwood Acad. Publ., 1988)
  65. ’’’?’?’?’?у ’’ ’K, ’’’?фsh’?ts ’M ’a ’lт’?т’?ст’?ch’?с’?’?ya ф’?’?’?’?’? Т. 1 (’a.: ’s’?’?’?’?т’?’?т, 2001); Landau L D, Lifshitz E M Statistical Physics Vol. 1 (Oxford: Pergamon Press, 1980)
  66. ’I’?’?’?’?’?’?’? ’G ’E ’Fурс т’?’?р’?’? ’?’?р’?yaт’?’?ст’?’? (’a.: ’p’i’l’l, 2001); Gnedenko B V Theory Of Probability (Amsterdam: Gordon and Breach Sci. Publ., 1980)
  67. ’G’?т’?’?’?’? ’I ’a ’? ’?р. ’z’?сь’?’? Zh’e’n’s 78 974 (2003); Batanov G M et al. JETP Lett. 78 502 (2003)
  68. Skvortsova N N et al. Plasma Phys. Control. Fusion 48 A393 (2006)
  69. She Z-S, Leveque E Phys. Rev. Lett. 72 336 (1994)
  70. Dubrulle B Phys. Rev. Lett. 73 959 (1994)
  71. Schertzer D, Lovejoy S, Hubert P Mathematical Problems In Environmental Science And Engineering (Ser. in Contemporary Applied Mathematics) Vol. 4 (Eds A Ern, L Weiping) (Beijing: Higher Education Press, 2002) p. 106
  72. Isichenko M B Rev. Mod. Phys. 64 961 (1992)
  73. Kraichnan R H J. Fluid Mech. 41 189 (1970)
  74. Kraichnan R H J. Fluid Mech. 5 497 (1959)
  75. ’Rр’?sh’?’?’?’?’? ’z ’l Astron. Zh. 40 742 (1963); Iroshnikov P S Sov. Astron. 7 566 (1964)
  76. Kraichnan R H Phys. Fluids 85 575 (1965)
  77. Goldreich P, Sridhar S Astrophys. J. 438 763 (1995)
  78. Schekochihin A A, Cowley S C Magnetohydrodynamics: Historical Evolution And Trends (Eds S Molokov, R Moreau, H K Moffatt) (Berlin: Springer, 2007) p. 85
  79. Boldyrev S Phys. Rev. Lett. 96 115002 (2006)
  80. Biskamp D, Müller W-C Phys. Plasmas 7 4889 (2000)
  81. Benzi R et al. Phys. Rev. E 48 R29 (1993)
  82. Schertzer D et al. Fractals 5 427 (1997)
  83. Schertzer D, Lovejoy S Physica A 338 173 (2004)
  84. Arneodo A, Bacry E, Muzy J F J. Math. Phys. 39 4142 (1998)
  85. She Z-S, Waymire E C Phys. Rev. Lett. 74 262 (1995)
  86. Politano H, Pouquet A, Carbone V Europhys. Lett. 43 516 (1998)
  87. Schertzer D, Lovejoy S, Hubert P "An introduction to stochastic multifractal fields" http://www.enpc.fr/multifractal/online/DS_course_0801.pdf
  88. Politano H, Pouquet A Geophys. Res. Lett. 25 273 (1998)
  89. Chen F F Introduction To Plasma Physics And Controlled Fusion (Berlin: Springer, 1984); Ch’?’? ’s ’E’?’?’?’?’?’?’? ’? ф’?’?’?’?у ’?’?’?’?’?ы (’a.: ’a’?р, 1987)
  90. ’Gу’?’?’?’? ’E ’z ’lт’?kh’?ст’?ch’?с’?’?’? ’?’?’?’?’?’? стру’?тур’?’?’? ’?’?’?’?’?’?’?’?’?’? тур’?у’?’?’?т’?’?ст’? (’z’?’? р’?’?. ’E Yu ’F’?р’?’?’?’?’?, ’v ’v ’l’?’?’?рts’?’?’?’?) (’a.: ’a’B’F’l ’zр’?сс, 2003) с. 125
  91. Budaev V P Czech. J. Phys. 48 (S3) 121 (1998)
  92. Boedo J A et al. Phys. Plasmas 8 4826 (2001)
  93. Budaev V P et al. J. Nucl. Mater. 176 - 177 705 (1990)
  94. Wagner F et al. Phys. Rev. Lett. 49 1408 (1982)
  95. Kuznetsov E A et al. ’z’?сь’?’? Zh’e’n’s 85 288 (2007); Kuznetsov E A et al. JETP Lett. 85 236 (2007)
  96. Savin S et al. Planet. Space Sci. 59 606 (2011)
  97. ’z’?стуkh’?’? ’E ’z, Chу’?’?’? ’v ’E ’z’?сь’?’? Zh’e’n’s 82 395 (2005); Pastukhov V P, Chudin N V JETP Lett. 82 356 (2005)
  98. Bak P, Tang C, Wiesenfeld K Phys. Rev. A 38 364 (1988)
  99. Budaev V P et al. Nucl. Fusion 46 S181 (2006)
  100. Clauser F H Adv. Appl. Mech. 56 1 (1956)
  101. Townsend A A The Structure Of Turbulent Shear Flow (Cambridge: Cambridge Univ. Press, 1956)
  102. Panton R (Ed.) Self-Sustaining Mechanisms Of Wall Turbulence (Southampton: Computational Mechanics Publ., 1997)
  103. Marusic I et al. Phys. Fluids 22 065103 (2010)
  104. Zagarola M V "Mean flow scaling in turbulent pipe flow" Ph.D. Thesis (Princeton: Princeton Univ. Press, 1996)
  105. Tsuji Y, Nakamura I Phys. Fluids 11 647 (1999)
  106. Monkewitz P A, Chauhan K A, Nagib H M Phys. Fluids 19 115101 (2007)
  107. Barenblatt G I et al. Proc. Natl. Acad. Sci. USA 94 7817 (1997)
  108. George W K, Castillo L Appl. Mech. Rev. 50 689 (1997)
  109. Klewicki J et al. Philos. Trans. R. Soc. London A 365 823 (2007)
  110. L’vov V S, Procaccia I, Rudenko O Phys. Rev. Lett. 100 054504 (2008)
  111. Zagarola M V, Smits A J J. Fluid Mech. 373 33 (1998)
  112. McKeon B J, Sreenivasan K R Philos. Trans. R. Soc. London A 365 635 (2007)
  113. Panton R L Prog. Aerospace Sci. 37 341 (2001)
  114. Adrian R J Phys. Fluids 19 041301 (2007)
  115. ’Iр’?’? ’I ’i, ’F’?’?’?’?’? ’E ’E, Ch’?р’?’?р’?’? ’E ’I ’pс’?. ’?’?kh’?’?’?’?’? 4 (1) 52 (2006)
  116. ’Oы’?’?’? ’F ’z ’? ’?р. Zh. Eksp. Teor. Fiz. 132 510 (2007); Zybin K P et al. JETP 105 455 (2007)
  117. Zybin K P et al. Phys. Rev. Lett. 100 174504 (2008)
  118. ’Oы’?’?’? ’F ’z ’? ’?р. Zh. Eksp. Teor. Fiz. 134 1024 (2008); Zybin K P et al. JETP 107 879 (2008)
  119. Zybin K P, Sirota V A, Ilyin A S Phys. Rev. E 82 056324 (2010)
  120. Zybin K P, Sirota V A Phys. Rev. Lett. 104 154501 (2010)
  121. Xu H et al. Phys. Rev. Lett. 96 024503 (2006)
  122. Sreenivasan K R Rev. Mod. Phys. 71 S383 (1999)
  123. Arneodo A et al. Europhys. Lett. 34 411 (1996)
  124. Klewicki J C, Foss J F, Wallace J M Flow At Ultra-High Reynolds And Rayleigh Numbers (Eds R J Donnelly, K R Sreenivasan) (New York: Springer, 1998) p. 450
  125. Nagib H M, Chauhan K A, Monkewitz P A Philos. Trans. R. Soc. London A 365 755 (2007)
  126. Carlier J, Stanislas M J. Fluid Mech. 535 143 (2005)
  127. Nickels T B et al. Phys. Rev. Lett. 95 074501 (2005)
  128. Maurer J, Tabeling P, Zocchi G Europhys. Lett. 26 31 (1994); Zocchi G et al. Phys. Rev. E 50 3693 (1994); Belin F, Tabeling P, Willaime H Physica D 93 52 (1996)
  129. Anselmet F et al. J. Fluid Mech. 140 63 (1984); Marchand M These INPG (Grenoble: National Polytechnical Inst. of Grenoble, 1993)
  130. Chabaud B et al. Phys. Rev. Lett. 73 3227 (1994)
  131. Baudet C, Ciliberto S, Phan N T J. Physique II 3 293 (1993)
  132. Van de Water W, Van der Vorst B, Van de Wetering E Europhys. Lett. 16 443 (1991)
  133. Camussi R et al. Phys. Fluids 8 1181 (1996)
  134. Lumley J L Phys. Fluids 8 1056 (1965)
  135. Dahm W J A, Southerland K B, Buch K A Phys. Fluids A 3 1115 (1991)
  136. Adrian R J Annu. Rev. Fluid Mech. 23 261 (1991)
  137. Batchelor G K, Townsend A A Proc. R. Soc. London A 199 238 (1949)
  138. Cadot O, Douady S, Couder Y Phys. Fluids 7 630 (1995)
  139. Camussi R et al. Phys. Fluids 8 1181 (1996)
  140. Camussi R et al. Phys. Fluids 20 075113 (2008)
  141. ’G’?р’?’?у’?’?’? ’E ’R ’B’?т’?р’?ф’?р’?т ’?’?сс. ... ’?’?’?т. ф’?’?.-’?’?т. ’?’?у’? (’v’?’?’?с’?’?’?рс’?: ’R’?ст’?тут т’?’?р’?т’?ch’?с’?’?’? ’? ’?р’?’?’?’?’?’?’?’? ’?’?kh’?’?’?’?’?, 2009)
  142. Meneveau ’l, Sreenivasan K R J. Fluid Mech. 224 429 (1991)
  143. Rosales ’l, Meneveau ’l Phys. Rev. E 78 016313 (2008)
  144. Lovejoy S, Schertzer D, Tuck A F Phys. Rev. E 70 036306 (2004)
  145. Chigirinskaya Y et al. Nonlin. Proces. Geophys. 1 105 (1994)
  146. Finn D et al. J. Appl. Meteor. 40 229 (2001)
  147. Schmitt F et al. C. R. Acad. Sci. Paris II 314 749 (1992)
  148. Schmitt F et al. Europhys. Lett. 34 195 (1996)
  149. Pelletier J Atmospheric And Oceanic Sciences (Montreal: McGill, 1995)
  150. Wang Y Atmospheric And Oceanic Sciences (Montreal: McGill, 1995)
  151. Benzi R, Biferale L J. Stat. Phys. 135 977 (2009)
  152. Frisch U, Vergassola M Europhys. Lett. 14 439 (1991)
  153. Biferale L et al. Phys. Rev. Lett. 93 064502 (2004)
  154. Sreenivasan K, Schumacher J Philos. Trans. R. Soc. London A 368 1561 (2010)
  155. Villermaux E, Sixou B, Gagne Y Phys. Fluids 7 2008 (1995)
  156. ’I’?’?’?’?’?р ’M ’G ’R’?’?. ’i’B’v ’s’?’?’?’?’? ’?т’?’?сф’?ры ’? ’?’?’?’?’?’? 41 733 (2005); Gledzer E B Izv. Atmos. Ocean. Phys. 41 667 (2005)
  157. Lee C B et al. Experiments In Fluids 28 243 (2000)
  158. Balakumar B J, Adrian R J Philos. Trans. R. Soc. London A 365 665 (2007)
  159. Kim K C, Adrian R J Phys. Fluids 11 417 (1999)
  160. McKeon B J, Morrison J F Philos. Trans. R. Soc. London A 365 771 (2007)
  161. Toh S, Itano T J. Fluid Mech. 524 249 (2005)
  162. Rao K N, Narasimha R, Badri Narayanan M A J. Fluid Mech. 48 339 (1971)
  163. Hutchins N, Marusic I Philos. Trans. R. Soc. London A 365 647 (2007)
  164. ’F’?ch’?’?’?’? Yu ’l, ’F’?’?’?’?’? ’E ’E, ’’’?’?ch’?’?’?’? ’E Ya ’E’?’?’?’?’?’?’?’?’?’?’?’? тур’?у’?’?’?т’?’?ст’? ’? ’?’?’?р’?’?’?ch’?’?’? с’?’?’? (’v’?’?’?с’?’?’?рс’?: ’v’?у’?’?, 1982)
  165. Klebanoff P S, Tidstrom K D, Sargent L M J. Fluid Mech. 12 1 (1962)
  166. Kachanov Y S Recent Results In Laminar-Turbulent Transition (Notes on Numerical Fluid Mechanics and Multidisciplinary Design) Vol. 86 (Eds S Wagner, M Kloker, U Rist) (Berlin: Springer-Verlag, 2004) p. 1
  167. Boiko A V et al. The Origin Of Turbulence In Near-Wall Flows (Berlin: Springer-Verlag, 2002)
  168. ’’’?т’?’?’?’?’?’?’? ’a ’E ’? ’?р. Priklad. Mekh. Tekh. Fiz. 45 (3) 50 (2004); Litvinenko M V et al. J. Appl. Mech. Tech. Phys. 45 349 (2004)
  169. ’’’?т’?’?’?’?’?’?’? Yu ’B ’? ’?р. ’n’?’?’?’?ф’?’?’?’?’? ’?эр’?’?’?kh’?’?’?’?’? 11 339 (2004); Litvinenko Yu A et al. Thermophys. Aeromech. 11 329 (2004)
  170. ’F’?’?’?’?’? ’E ’E ’? ’?р. Priklad. Mekh. Tekh. Fiz. 43 (2) 62 (2002); Kozlov V V et al. J. Appl. Mech. Tech. Phys. 43 224 (2002)
  171. Jiménez J Annu. Rev. Fluid Mech. 36 173 (2004)
  172. ’F’?р’?’?’?’?’? ’E ’R ’n’?’?’?’?ф’?’?’?’?’? ’?эр’?’?’?kh’?’?’?’?’? 12 183 (2005); Kornilov V I Thermophys. Aeromech. 12 175 (2005)
  173. Chernyshov A A, Karelsky K V, Petrosyan A S Phys. Plasmas 17 102307 (2010)
  174. Chernyshov A A, Karelsky K V, Petrosyan A S Phys. Fluids 19 055106 (2007)
  175. Moin P, Mahesh K Annu. Rev. Fluid Mech. 30 539 (1998)
  176. Wu X, Moin P J. Fluid Mech. 630 5 (2009)
  177. Jiménez J, Moser R D Philos. Trans. R. Soc. London A 365 715 (2007)
  178. Schlatter P et al. Phys. Fluids 21 051702 (2009)
  179. Hu Z, Morfey C L, Sandham N D AIAA J. 44 1541 (2006)
  180. Abe H, Kawamura H, Choi H J. Fluids Eng. 126 835 (2004)
  181. Hutchins N, Marusic I J. Fluid Mech. 579 1 (2007)
  182. Marusic I, Heuer W D C Phys. Rev. Lett. 99 114504 (2007)
  183. Yakhot V, Sreenivasan K R J. Stat. Phys. 121 823 (2005)
  184. Toschi F, Bodenschatz E Annu. Rev. Fluid Mech. 41 375 (2009)
  185. Biferale L et al. Phys. Fluids 20 065103 (2008)
  186. Benzi R et al. J. Fluid Mech. 653 221 (2010)
  187. Voth G A et al. J. Fluid Mech. 469 121 (2002)
  188. Biferale L et al. Phys. Fluids 17 021701 (2005)
  189. Paschmann G et al. J. Geophys. Res. 81 2883 (1976)
  190. Haerendel G J. Atmos. Terrestr. Phys. 40 343 (1978)
  191. ’B’?т’?’?’?’?’? ’B ’M, Sh’?’?’?’?с’?’?’? ’E ’z ’I’?’?’?’?’?’?. ’?эр’?’?’?’?’?ya 15 297 (1975); Antonova A E, Shabanskii V P Geomagn. Aeron. 15 243 (1975)
  192. Spreiter J R, Briggs B R J. Geophys. Res. 67 37 (1962)
  193. Savin S P et al. Geospace Mass And Energy Flow: Results From The Intern. Solar-Terrestrial Physics Program (Geophysical Monograph) Vol. 104 (Eds J L Horwitz, D L Gallagh, W K Peterson) (Washington, DC: AGU, 1998) p. 25
  194. ’z’?’?’?’? ’M ’E ’? ’?р. ’F’?с’?’?ch. ’?сс’?’?’?. 45 285 (2007); Panov E V et al. Cosmic Res. 45 268 (2007)
  195. Savin S et al. Nonlin. Proces. Geophys. 13 377 (2006)
  196. Nedospasov A V J. Nuclear Materials 196 - 198 90 (1992)
  197. Chen F F Plasma Diagnostic Techniques (Eds R H Huddlestone, S L Leonard) (New York: Academic Press, 1965) p. 113; Ch’?’? ’s ’K’?’?’?’?’?ст’?’?’? ’?’?’?’?’?ы ’z’?’? р’?’?. ’i Kh’?’?’?’?ст’?у’?’?, ’l ’’’?’?’?’?р’?’?) (’a.: ’a’?р, 1967) с. 94
  198. Stangeby P C The Plasma Boundary Of Magnetic Fusion Devices (London: Taylor & Francis, 2000)
  199. Hutchinson I H Principles Of Plasma Diagnostics (Cambridge: Cambridge Univ. Press, 2002)
  200. Vershkov V A, Grashin S A, Chankin A V J. Nucl. Mater. 145 - 147 611 (1987)
  201. Budaev V P, Ivanov R S J. Nucl. Mater. 162 - 164 322 (1989)
  202. Sh’?т’?’?’?’? ’l ’E ’? ’?р. Fiz. Plazmy 33 195 (2007); Shatalin S V et al. Plasma Phys. Rep. 33 169 (2007)
  203. Watkins J G et al. Rev. Sci. Instrum. 63 4728 (1992)
  204. Huber A et al. Plasma Phys. Control. Fusion 47 409 (2005)
  205. Gonçalves B et al. J. Nucl. Mater. 337 - 339 376 (2005)
  206. Antar G Y et al. Phys. Plasmas 10 419 (2003)
  207. Asakura N et al. Phys. Rev. Lett. 84 3093 (2000)
  208. Endler M et al. Phys. Scripta 51 610 (1995)
  209. Antar G Y, Counsell G, Ahn J-W Phys. Plasmas 12 082503 (2005)
  210. Skvortsova N N et al. Plasma Phys. Control. Fusion 48 A393 (2006)
  211. ’G’?т’?’?’?’? ’I ’a ’? ’?р. ’z’?сь’?’? Zh’e’n’s 73 143 (2001); Batanov G M et al. JETP Lett. 73 126 (2001)
  212. Tanaka K et al. Nucl. Fusion 46 110 (2006)
  213. Alonso J A et al. Plasma Phys. Control. Fusion 48 B465 (2006)
  214. Carter T A Phys. Plasmas 13 010701 (2006)
  215. Chiu J S, Sen A K Phys. Plasmas 7 4492 (2000)
  216. Antoni V et al. Phys. Rev. Lett. 80 4185 (1998)
  217. Ohno N et al. Contrib. Plasma Phys. 44 222 (2004)
  218. Schmitz L et al. J. Nucl. Mater. 176 - 177 522 (1990)
  219. Boedo J A et al. Rev. Sci. Instrum. 70 2997 (1999)
  220. Biewer T M et al. Rev. Sci. Instrum. 75 650 (2004)
  221. Zweben S J, Taylor R J Nucl. Fusion 21 193 (1981)
  222. Graessle D E, Prager S C, Dexter R N Phys. Fluids B 3 2626 (1991)
  223. Stöckel J et al. Plasma Phys. Control. Fusion 41 A577 (1999)
  224. ’z’?тр’?’? ’B ’M ’? ’?р. ’lт’?kh’?ст’?ch’?с’?’?’? ’?’?’?’?’?’? стру’?тур’?’?’? ’?’?’?’?’?’?’?’?’?’? тур’?у’?’?’?т’?’?ст’? (’z’?’? р’?’?. ’E Yu ’F’?р’?’?’?’?’?, ’v ’v ’l’?’?’?рts’?’?’?’?) (’a.: ’a’B’F’l ’zр’?сс, 2003) с. 7
  225. ’Gу’?’?’?’? ’E ’z ’zут’? уch’?’?’?’?’?. ’M.’z. ’E’?’?’?kh’?’? (’zр’?’?с. р’?’?’?’?’?. ’E ’z ’l’?’?р’?’?’?) (’a.: ’i’vTs "’Fурch’?т’?’?с’?’?’? ’?’?ст’?тут" (2007) с. 64
  226. ’Gу’?’?’?’? ’E ’z Fiz. Plazmy 25 668 (1999); Budaev V P Plasma Phys. Rep. 25 610 (1999)
  227. Terry J L et al. Phys. Plasmas 10 1739 (2003)
  228. McKee G R et al. Rev. Sci. Instrum. 75 3490 (2004)
  229. Zweben S J et al. Phys. Plasmas 13 056114 (2006)
  230. Bleuel J et al. New J. Phys. 4 38 (2002)
  231. Huber A et al. J. Nucl. Mater. 266 - 269 546 (1999)
  232. Terry P W, Newman D E, Ware A S Phys. Plasmas 10 1066 (2003)
  233. McKee G R et al. Nucl. Fusion 41 1235 (2001)
  234. Zweben S J, Medley S S Phys. Fluids B 1 2058 (1989)
  235. Winslow D L et al. Rev. Sci. Instrum. 68 396 (1997)
  236. Thomsen H et al. Phys. Plasmas 9 1233 (2002)
  237. Zweben S J et al. J. Nucl. Mater. 145 - 147 250 (1987)
  238. Windisch T, Grulke O, Klinger T J. Nucl. Mater. 390 - 391 395 (2009)
  239. Surko C M, Slusher R E Science 221 817 (1983)
  240. Liewer P C Nucl. Fusion 25 543 (1985)
  241. Wootton A J et al. Phys. Fluids B 2 2879 (1990)
  242. Endler M J. Nucl. Mater. 266 - 269 84 (1999)
  243. Horton W Rev. Mod. Phys. 71 735 (1999)
  244. Endler M Plasma Phys. Control. Fusion 41 1431 (1999)
  245. Rhodes T L, Ritz C P, Bengtson R D Nucl. Fusion 33 1147 (1993)
  246. Ritz Ch P et al. Phys. Rev. Lett. 62 1844 (1989)
  247. Boedo J A et al. Phys. Plasmas 8 4826 (2001)
  248. Grulke O et al. Phys. Plasmas 13 012306 (2006)
  249. Kirnev G S et al. J. Nucl. Mater. 337 - 339 352 (2005)
  250. Budaev V P, Ivanov R S J. Nucl. Mater. 162 - 164 322 (1989)
  251. Budaev et al. Plasma Phys. Control. Fusion 35 429 (1993)
  252. Heller M V A P et al. Phys. Plasmas 6 846 (1999)
  253. Sudo S et al. Plasma Phys. Control. Fusion 45 A425 (2003)
  254. Masuzaki S et al. Nucl. Fusion 42 750 (2002)
  255. Budaev V P et al. Plasma Phys. Control. Fusion 50 074014 (2008)
  256. ’Gу’?’?’?’? ’E ’z, Kh’?’?ch’?’?’?’? ’’ ’v Zh. Eksp. Teor. Fiz. 131 711 (2007); Budaev V P, Khimchenko L N JETP 104 629 (2007)
  257. Skvortsova N N et al. Plasma Phys. Control. Fusion 48 A393 (2006)
  258. ’Gу’?’?’?’? ’E ’z, ’R’?’?’?’?’? ’i ’l Fiz. Plazmy 17 1332 (1991)
  259. Carreras B A, Lynch V E, LaBombard B Phys. Plasmas 8 3702 (2001)
  260. Antar G Y et al. Phys. Rev. Lett. 87 065001 (2001)
  261. ’Gу’?’?’?’? ’E ’z, Kh’?’?ch’?’?’?’? ’’ ’v ’E’?’?р. ’?т’?’?’?’?’? ’?’?у’?’? т’?kh’?’?’?’? ’n’?р’?’?ya’?’?р’?’?’? с’?’?т’?’? (3) 34 (2008)
  262. Ottino J M The Kinematics Of Mixing: Stretching, Chaos, And Transport (Cambridge: Cambridge Univ. Press, 1989)
  263. ’Bр’?’?’?ь’? ’E ’R ’n’?’?р’?ya ’?’?т’?стр’?ф (’a.: ’v’?у’?’?, 1990); Arnold V I Catastrophe Theory (Berlin: Springer-Verlag, 2004)
  264. ’’’?с’?ут’?’? ’B Yu Usp. Fiz. Nauk 177 989 (2007); Loskutov A Phys. Usp. 50 939 (2007)
  265. Jokipii J R Astrophys. J. 146 480 (1966)
  266. Schuster H G Deterministic Chaos (Weincheim: Physik-Verlag, 1984); Shуст’?р ’I ’K’?т’?р’?’?’?’?р’?’?’?’?’?ы’? kh’?’?с (’a.: ’a’?р, 1988)
  267. ’Fу’?’?’?ts’?’? ’l ’z ’K’?’?’?’?’?ch’?с’?’?’? kh’?’?с (’a.: ’s’?’?’?’?т’?’?т, 2001)
  268. Budaev V P et al. Proc. 22nd European Physical Society Conf. on Controlled Fusion and Plasma Physics, Bornemouth, UK, 1995, Pt. I, p. I-277
  269. ’’’?с’?ут’?’? ’B Yu ’E’?ст’?. ’a’I’p 3 ’s’?’?. ’Bстр’?’?. (2) 3 (2001)
  270. Ott E, Grebogi C, Yorke J A Phys. Rev. Lett. 64 1196 (1990)
  271. Pyragas K Phys. Lett. A 170 421 (1992)
  272. Zajac J et al. Czech. J. Phys. 55 1615 (2005)
  273. Finken K H, Eich T, Kaleck A Nucl. Fusion 38 515 (1998)
  274. Budaev V P et al. J. Nucl. Mater. 313 - 316 1309 (2003)
  275. Budaev V P Proc. 2nd Europhysics Workshop on the Role of Electric Fields in Plasma Confinement and Exhaust, Maastricht, The Netherlands, 19 - 20 June 1999
  276. Budaev V et al. Nucl. Fusion 44 S108 (2004)
  277. ’Gу’?’?’?’? ’E ’z Fiz. Plazmy 34 867 (2008); Budaev V P Plasma Phys. Rep. 34 799 (2008)
  278. Muzy J F, Bacry E, Arneodo A Phys. Rev. E 47 875 (1993)
  279. Arneodo A, Muzy J F, Roux S G J. Physique France II 7 363 (1997)
  280. Bacry E, Muzy J F, Arnéodo A J. Stat. Phys. 70 635 (1993)
  281. Budaev V P et al. Plasma Fusion Res. 3 S1019 (2008)
  282. Budaev V P Contrib. Plasma Phys. 50 218 (2010)
  283. Muzy J F, Bacry E, Arneodo A Phys. Rev. Lett. 67 3515 (1991)
  284. Budaev V P et al. Proc. 34th EPS Conf. on Plasma Physics Warsaw, 2 - 6 July 2007 ECA Vol. 31F p. 1.088
  285. Budaev V P et al. Contrib. Plasma Phys. 48 42 (2008)
  286. ’G’?zh’?’?’?’? ’l ’E, ’z’?рsh’?’? ’K ’B ’sр’?’?т’?’?ы ’? ’?у’?ьт’?фр’?’?т’?’?ы (’a. - ’Rzh’?’?с’?: ’iKh’K, 2001)
  287. Budaev V P Physica A 344 299 (2004)
  288. Muüller W-C, Biskamp D Phys. Rev. Lett. 84 475 (2000)
  289. Antar G Y Phys. Rev. Lett. 91 055002 (2003)
  290. Sorriso-Valvo L et al. Europhys. Lett. 75 832 (2006)
  291. Müller W-C, Biskamp D, Grappin R Phys. Rev. E 67 066302 (2003)
  292. Frisch U et al. J. Fluid Mech. 68 769 (1975)
  293. Budaev V P et al. Nucl. Fusion 46 S181 (2006)
  294. Masuzaki S et al. J. Nucl. Mater. 313 - 316 852 (2003)
  295. She Z-S, Waymire E C Phys. Rev. Lett. 74 262 (1995)
  296. Mason J, Cattaneo F, Boldyrev S Phys. Rev. Lett. 97 255002 (2006)
  297. Lovejoy S, Schertzer D, Silas P Water Resour. Res. 34 3283 (1998)
  298. Petrukovich A A Nonequilibrium Phenomena In Plasmas (Eds A S Sharma, P K Kaw) (Dordrecht: Springer, 2005) p. 145
  299. Vörös Z et al. Nonlin. Proces. Geophys. 14 535 (2007)
  300. Treumann R A Geophys. Res. Lett. 24 1727 (1997)

© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions