Issues

 / 

1996

 / 

December

  

Reviews of topical problems


Quantum field renormalization group in the theory of fully developed turbulence

 a,  a,  a, b, c
a Department of Theoretical Physics, Institute of Physics, St. Petersburg State University, ul. Ulyanovskaya 1, Petrodvorez, St. Petersburg, 198904, Russian Federation
b Lomonosov Moscow State University, Vorobevy Gory, Moscow, 119991, Russian Federation
c Lomonosov Moscow State University, Department of Physics, Leninskie Gory 1 build. 2, Moscow, 119991, Russian Federation

Quantum field renormalisation group results of the theory of developed turbulence are reviewed. Background information about quantum field renormalisation theory, including operator expansion and the renormalisation of composite operators is given. As an example problem, the stochastic model of isotropic homogeneous turbulence is considered for which, using the renormalisation technique, the existence of infrared scaling with Kholmogorov dimensions is proved. The dimension of composite operators and the infrared asymptotic behaviour of various correlation functions are discussed, and numerical amplitude factors of scaling laws are calculated.

Fulltext is available at IOP
PACS: 03.40.Ge, 47.10.+g
DOI: 10.1070/PU1996v039n12ABEH000183
URL: https://ufn.ru/en/articles/1996/12/a/
Citation: Adzhemyan L T, Antonov N V, Vasil’ev A N "Quantum field renormalization group in the theory of fully developed turbulence" Phys. Usp. 39 1193–1219 (1996)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Аджемян Л Ц, Антонов Н В, Васильев А Н «Квантово-полевая ренормализационная группа в теории развитой турбулентности» УФН 166 1257–1284 (1996); DOI: 10.3367/UFNr.0166.199612a.1257

References (122) ↓ Cited by (70) Similar articles (20)

  1. Monin A S, Yaglom A M Statisticheskaya Gidrodinamika (Statistical Fluid Mechanics) Ch. 2 (Moscow: Nauka, 1967) [Translated into English Vol. 2 (Cambridge, MA: MIT Press, 1975)]
  2. Orszag S A, in Fluid Dynamics, Les Houches, 1973 (Eds R Balian, J-L Peube, London: Gordon and Breach,1977) p. 235
  3. McComb W D The Physics of Fluid Turbulence (Oxford: Clarendon, 1990); McComb W D Rep. Prog. Phys. 58 1117 (1995)
  4. Landau L D, Lifshits E M Gidrodinamika (Hydrodynamics, Moscow: Nauka,1986) [Translated into English Landau L D, Lifshitz E M Fluid Mechanics (London: Pergamon Press, 1959)]
  5. Bogoliubov N N, Shirkov D V Introduction to the Theory of Quantized Fields (New York: A Willey Interscience, 1959, 1980)
  6. Collins J C Renormalization (Cambridge: Cambridge Univ. Press, 1984) [Translated into Russian (Moscow: Mir, 1988)]
  7. Patashinskiî A Z, Pokrovskiî V L Fluktuatsionnaya Teoriya Fazovykh Perekhodov ( Fluctuation Theory of Phase Transitions, Moscow: Nauka, 1982)
  8. Brezin E, Le Guillou J C, Zinn-Justin J, in Phase Transitions and Critical Phenomena Vol. 6 (Eds C Domb, M S Green, New York: Academic, 1976) p. 125
  9. Amit D J Field Theory, the Renormalization Group, and Critical Phenomena (New York: McGraw-Hill, 1978)
  10. Zinn-Justin J Quantum Field Theory and Critical Phenomena (New York: Clarendon, 1996)
  11. Popov V N Kontinual’nye Integraly v Kvantovoî Teorii Polya i Statisticheskoî Fizike (Functional Integral in Quantum Field Theory and Statistical Physics, Moscow: Atomizdat, 1976)
  12. Vasil’ev A N Funktsional’nye Metody v Kvantovoî Teorii Polya i Statistike (Functional Methods in Quantum Field Theory and Statistical Mechanics, Leningrad: Leningrad Univ. Press, 1976) [Translated into English (Gordon & Breach, in press)]
  13. Kraichnan R H J. Fluid. Mech. 5 407 (1959)
  14. Wyld H W Ann. Phys. 14 143 (1961); 9 1728, 1884 (1966)
  15. Adzhemyan L Ts, Antonov N V, Vasiliev A N Zh. Eksp. Teor. Fiz. 95 1272 (1989) [Sov. Phys. JETP 68 733 (1989)]
  16. De Dominicis C, Martin P C Phys. Rev. A 19 419 (1979)
  17. Janssen H K Z. Phys. B 23 377 (1976); Bausch R, Janssen H K, Wagner H Z. Phys. B 24 113 (1976)
  18. De Dominicis C J. Phys. (Paris) 37 C1-247 (1976); De Dominicis C, Peliti L Phys. Rev. B 18 353 (1978)
  19. Adzhemyan L Ts, Vasiliev A N, Pis’mak Yu M Teor. Mat. Fiz. 57 268 (1983) [Theor. Math. Phys. 57 1131 (1983)]
  20. Keldysh L V Zh. Eksp. Teor. Fiz. 47 1515 (1964) [Sov. Phys. JETP 20 1018 (1965)]
  21. Martin P C, Siggia E D, Rose H A Phys. Rev. A 8 423 (1973)
  22. Zakharov V E, L’vov V S Izv. Vyssh. Uchebn. Zaved. Radiofiz. 18 1470 (1975) [Radiophys. Quantum Electron.]
  23. Hohenberg P C, Halperin B I Rev. Mod. Phys. 49 435 (1977)
  24. Ronis D Phys. Rev. A 36 3322 (1987)
  25. Olla P Phys. Rev. Lett. 67 2465 (1991)
  26. Honkonen J, Nalimov M Yu Z. Phys. B 99 297 (1996)
  27. Teodorovich E V Izv. Akad. Nauk SSSR Ser. Mekh. Zhidk. Gaza 22 29 (1987) [Fluid Dyn. 22 517 (1987)]; Dokl. Akad. Nauk SSSR 299 836 (1988)
  28. Teodorovich E V Zh. Eksp. Teor. Fiz. 96 163 (1989) [Sov. Phys. JETP 69 89 (1989)]
  29. Fournier J-D, Frish U Phys. Rev. A 28 1000 (1983)
  30. Wilson K, Kogut J The Renormalization Group and the epsilon-Expansion (New York: Wiley, 1974) [Translated into Russian (Moscow: Mir, 1975)] [Also Phys. Rep. C 12 (2) 79 (1974)]
  31. Yakhot V, Orszag S A Phys. Rev. Lett. 57 1722 (1986)
  32. Yakhot V, Orszag S A J. Sci. Comput. 1 3 (1986)
  33. Dannevik W P, Yakhot V, Orszag S A Phys. Fluids 30 2021 (1987)
  34. Antonov N V Zapiski Nauchnykh Seminarov LOMI 164 3 (1987)
  35. Antonia R A, Satyaprakash B R, Hussian A K M F J. Fluid. Mech. 119 55 (1982)
  36. Anselmet F, Gagne Y, Hopfinger E J, Antonia R A J. Fluid. Mech. 140 63 (1984)
  37. Kuznetsov V R, Sabel’nikov V A Turbulentnost’ i Gorenie (Turbulence and Combusion, Moscow: Nauka, 1986) [Translated into English (New York: Hemisphere Publ. Corp., 1990)]
  38. Kuznetsov V R, Praskovskiî A A, Sabel’nikov V A Izv. Akad. Nauk SSSR Ser. Mekh. Zhidk. Gaza 23 (6) 51 (1988) [Fluid. Dyn. 23 843 (1988)]
  39. Halperin B I, Hohenberg P C, Siggia E D Phys. Rev. B 13 1299 (1976)
  40. Adzhemyan L Ts, Vasil’ev A N, Gnatich M Teor. Mat. Fiz. 74 180 (1988) [Theor. Math. Phys.74 180 (1988)]
  41. Antonov N V Vestn. St. Petersburg Univ. Fiz. Khim. (4) 6 (1992)
  42. Adzhemyan L Ts, Antonov N V, Kim T L Teor. Mat. Fiz. 100 382 (1994) [Theor. Math. Phys. 100 1086 (1994)]
  43. Adzhemyan L Ts, Borisenok S V, Girina V I Teor. Mat. Fiz. 105 450 (1995)
  44. Antonov N V Zapiski Nauchnykh Seminarov LOMI 169 18 (1988)
  45. Yakhot V, She Z-S, Orszag S A Phys. Fluids A 1 (2) 289 (1989)
  46. Yakhot V, Smith L M J. Sci. Comp. 7 35 (1992)
  47. Antonov N V, Borisenok S V, Girina V I Teor. Mat. Fiz. 106 92 (1996) [Theor. Math. Phys. 106 75 (1996)]
  48. Adzhemyan L Ts et al. Zapiski Nauchnykh Seminarov LOMI 224 43 (1995)
  49. Antonov N V, Vasil’ev A N Teor. Mat. Fiz. 110 122 (1997) [Theor. Math. Phys.]
  50. L’vov V S, Preprint No. 53 IAiE (Novosibirsk: IAiE, SO AN SSSR, 1977)
  51. Belinicher V I, L’vov V S Zh. Eksp. Teor. Fiz. 93 533 (1987) [Sov. Phys. JETP 66 303 (1987)]; L’vov V S Phys. Rep. 207 1 (1991)
  52. Moiseev S S et al. Dokl. Akad. Nauk SSSR 271 856 (1983) [Sov. Phys. Dokl. 28 634 (1983)]; Moiseev S S, Tur A V, Yanovskiî V V Dokl. Akad. Nauk SSSR 279 96 (1984) [Sov. Phys. Dokl. 29 926 (1984)]
  53. Sagdeev R Z et al., in Nonlinear Effects in Plasma Physics and Hydrodynamics (Ed. R Z Sagdeev, Moscow: Mir, 1986) p. 138
  54. Tur A V, Yanovskiî V V, Preprint IKI Pr-1203 (Moscow: IKI AN SSSR, 1986)
  55. Antonov N V Zh. Eksp. Teor. Fiz. 105 614 (1994) [JETP 78 327 (1994)]
  56. Antonov N V Zapiski Nauchnykh Seminarov LOMI 189 15 (1991)
  57. Antonov N V Vestn. St. Petersburg Univ. Fiz. Khim. (3) 3 (1992)
  58. Adzhemyan L V, Adzhemyan L Ts Zapiski Nauchnykh Seminarov LOMI 224 36 (1995)
  59. Smith L M, Reynolds W C Phys. Fluids A 4 (2) 364 (1992)
  60. Kraichnan R H Phys. Fluids 30 2400 (1987)
  61. Kraichnan R H J. Fluid. Mech. 9 1728 (1966)
  62. Fournier J-D, Frish U Phys. Rev. A 17 747 (1978)
  63. L’vov V, Falkovich G Phys. Rev. A 46 4762 (1992)
  64. Adzhemyan L V, Adzhemyan L Ts Vestn. St. Petersburg Univ. Fiz. Khim. (3) 3 (1994)
  65. Adzhemyan L Ts, Nalimov M Yu Teor. Mat. Fiz. 91 294 (1992)
  66. Martin P C, De Dominicis C Prog. Theor. Phys. Suppl. (64) 108 (1978)
  67. Carati D Phys. Rev. A 41 3129 (1990)
  68. Liao W J. Phys. A 22 L737 (1989); Ohkitani K Phys. Fluids A 2 (9) 1529 (1990); Shivamoggi B J. Phys. A 23 1689 (1990); Novikov E A Phys. Lett. A 162 385 (1992)
  69. Yaglom A M Izv. Akad. Nauk SSSR. Fiz. Atmosfery i Okeana 17 1235 (1981)
  70. Lam S H Phys. Fluids A 4 (5) 1007 (1992)
  71. Zhou Y, Vahala G, Hossain M Phys. Rev. A 40 5865 (1989)
  72. Carati D Phys. Fluids A 2 1854 (1990)
  73. Giles M J Phys. Fluids 6 (2) 595 (1994)
  74. Staroselsky I et al. Phys. Rev. Lett. 65 171 (1990)
  75. Yakhot V, Orszag S A, She Z-S Phys. Fluids A 1 (2) 184 (1989)
  76. Yakhot V Phys. Fluids A 1 (2) 175 (1989)
  77. Yakhot V, Orszag S A Phys. Fluids 30 (1) 3 (1987)
  78. Eyink G L Phys. Fluids 6 (9) 3063 (1994)
  79. Borgas M S Phys. Fluids A 4 (9) 2055 (1992)
  80. Adzhemyan L Ts, Antonov N V Vestn. St. Petersburg Univ. Fiz. Khim. (2) 53 (1994)
  81. Yakhot V Phys. Rev. A 23 1486 (1981)
  82. Yakhot V Phys. Rev. A 24 3268 (1981)
  83. Levich E Phys. Lett. A 79 171 (1980)
  84. Grossmann S, Schnedler E Z. Phys. B 26 307 (1977)
  85. Teodorovich E V Zh. Eksp. Teor. Fiz. 102 863 (1992) [Sov. Phys. JETP 75 472 (1992)]
  86. Forster D, Nelson D R, Stephen M J Phys. Rev. Lett. 36 867 (1976); Phys. Rev. A 16 732 (1977)
  87. Rubinstein R, Barton J M Phys. Fluids 30 2987 (1987)
  88. Carati D, Brenig L Phys. Rev. A 40 5193 (1989)
  89. Adzhemyan L Ts et al. Int. J. Mod. Phys B 9 3401 (1995)
  90. Kim T L, Serdyukov A V Teor. Mat. Fiz. 105 412 (1995)
  91. Busa J et al., Preprint JINR E17-95-348 (Dubna: JINR, 1995); Helsinki University Preprint HU-TFT-96-19 (Helsinki: Helsinki University, 1996)
  92. Pouquet A, Fournier J-D, Sulem P-L J. Phys. Lett. (France) 39 L-199 (1978)
  93. Adzhemyan L Ts et al. J. Phys. II France 5 1077 (1995)
  94. Adzhemyan L Ts, Nalimov M Yu, Stepanova M M Teor. Mat. Fiz. 104 260 (1995) [Theor. Math. Phys. 104 971 (1995)]
  95. Volchenkov D Yu, Nalimov M Yu Teor. Mat. Fiz. 106 375 (1996)
  96. Antonov N V, Nalimov M Yu, Udalov A A, Preprint SPbU PI-11-96 (St. Petersburg: SPbGU, 1996) [Submitted to Teor. Mat. Fiz.]
  97. Adzhemyan L Ts, Nalimov M Yu Teor. Mat. Fiz. 96 150 (1993) [Theor. Math. Phys. 96 872 (1993)]
  98. Adzhemyan L Ts, Borisenok S V, Nalimov M Yu Teor. Mat. Fiz. 106 416 (1996) [Theor. Math. Phys. 106 341 (1996)]
  99. Adzhemyan L Ts, Gnatich M, Steglik M, Preprint OIYaI P17-94-319 (Dubna: OIYaI, 1994)
  100. Nalimov M Yu, Ryzhov A K Vestn. St. Petersburg Univ. Fiz. Khim. (1) 72 (1995)
  101. McComb W D, Watt A G Phys. Rev. A 45 3507 (1992); 46 4797 (1992)
  102. Antonov N V, Borisenok S V, Girina B I Teor. Mat. Fiz. 107 47 (1996)
  103. Adzhemyan L Ts, Vasil’ev A N, Gnatich M Teor. Mat. Fiz. 58 72 (1984) [Theor. Math. Phys. 58 47 (1984)]
  104. Teodorovich E V Prikl. Mat. Mekh. 52 218 (1988) [Appl. Math. Mech. 52 170 (1988)]
  105. Gnatich M Teor. Mat. Fiz. 83 374 (1990)
  106. Fournier J-D, Sulem P-L, Pouquet A J. Phys. A 15 1393 (1982)
  107. Adzhemyan L Ts, Vasil’ev A N, Gnatich M Teor. Mat. Fiz. 64 196 (1985) [Theor. Math. Phys. 64 777 (1985)]
  108. Camargo S J, Tasso H Phys. Fluids B 4 (5) 1199 (1992)
  109. Adzhemyan L Ts, Volchenkov D Yu, Nalimov M Yu Teor. Mat. Fiz. 107 142 (1996)
  110. Adzhemyan L Ts, Vasil’ev A N, Gnatich M Teor. Mat. Fiz. 72 369 (1987) [Theor. Math. Phys. 72 940 (1987)]
  111. Pelletier G J. Plasma Phys. 24 421 (1980)
  112. Adzhemyan L Ts et al. Teor. Mat. Fiz. 78 368 (1989) [Theor. Math. Phys. 78 260 (1989)]
  113. Adzhemyan L Ts et al. Czechoslovak J.Phys. 45 491 (1995)
  114. Rose H A J. Fluid. Mech. 81 719 (1977)
  115. Siggia E D J. Fluid. Mech. 107 375 (1981)
  116. Eyink G L Phys. Rev. E 48 1823 (1993)
  117. Polyakov A M Nucl. Phys. B 396 367 (1993)
  118. Falkovich G, Hannany A Phys. Rev. Lett. 71 3454 (1993)
  119. Eyink G L Phys. Lett. A 172 355 (1993)
  120. Lebedev V V, L’vov V S Pis’ma Zh. Eksp. Teor. Fiz. 59 546 (1994) [JETP Lett. 59 577 (1994)]
  121. Antonov N V Vestn. St. Petersburg Univ. Fiz. Khim. (2) 74 (1996)
  122. Avellaneda M, Majda A J Commun. Math. Phys. (West Germ.) 131 381 (1990)

© 1918–2022 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions