RSS feeds
РусскийEnglish
Issue 12, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2015

 / 

June

←  →

Reviews of topical problems


Stretching vortex filaments model and the grounds of statistical theory of turbulence

,
Lebedev Physical Institute, Russian Academy of Sciences, Leninsky prosp. 53, Moscow, 119991, Russian Federation

Although statistical properties of small-scale velocity perturbations in homogeneous and isotropic hydrodynamic turbulence are well studied experimentally and numerically, no definite theoretical explanation is available yet. The concept of breaking vortices commonly accepted as the primary turbulent mechanism not only fails to account for a number of facts but also is self-contradictory. This review discusses an alternative concept according to which the stretching of vortices rather than their decay is the determining process. The evolution of stretching vortex filaments and their properties are derived directly from the Navier—Stokes equation. The model of stretching vortex filaments explains the power-law behavior of velocity structure functions and the intermittency of their exponents, thus imparting physical meaning to multifractal theory which is based on dimensional considerations. The vortex filaments model is the only theory that explains the observed differences between the scaling exponents of longitudinal and transverse structure functions.

Fulltext pdf (655 KB)
Fulltext is also available at DOI: 10.3367/UFNe.0185.201506b.0593
Keywords: hydrodynamics, turbulence, statistical theory
PACS: 47.10.ad, 47.27.Jv (all)
DOI: 10.3367/UFNe.0185.201506b.0593
URL: https://ufn.ru/en/articles/2015/6/b/
000361014200002
2015PhyU...58..556Z
Citation: Zybin K P, Sirota V A "Stretching vortex filaments model and the grounds of statistical theory of turbulence" Phys. Usp. 58 556–573 (2015)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 20th, January 2015, 20th, January 2015

Оригинал: Зыбин К П, Сирота В А «Модель вытягивающихся вихрей и обоснование статистических свойств турбулентности» УФН 185 593–612 (2015); DOI: 10.3367/UFNr.0185.201506b.0593

References (64) ↓ Cited by (27) Similar articles (20)

  1. Kolmogorov A N Dokl. Akad. Nauk SSSR 32 (1) 19 (1941); Perevod na angl. yaz, Kolmogorov A N Selected Works Of A. N. Kolmogorov Vol. 1 (Dordrecht: Kluwer Acad. Publ., 1991) p. 324
  2. Kolmogorov A N Dokl. Akad. Nauk SSSR 30 (4) 299 (1941); Perevod na angl. yaz., Kolmogorov A N Proc. R. Soc. Lond. A 434 9 (1991)
  3. Landau L D, Lifshits E M Gidrodinamika (M.: Nauka, 1986); Landau L D, Lifshitz E M Fluid Mechanics (Oxford: Pergamon Press, 1987)
  4. Frish U Turbulentnost’. Nasledie A.N. Kolmogorova (M.: FAZIS, 1998); Frisch U Turbulence. The Legacy Of A.N. Kolmogorov (Cambridge: Cambridge Univ. Press, 1995)
  5. Gurvich A S Izv. AN SSSR. Ser. Geofiz. 7 1042 (1960)
  6. Champagne F H J. Fluid Mech. 86 67 (1978)
  7. 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)
  8. Benzi R et al. J. Fluid Mech. 653 221 (2010)
  9. Gotoh T, Fukayama D, Nakano T Phys. Fluids 14 1065 (2002)
  10. Herweijer J A, van de Water W Advances in Turbulence V. Proc. of the Fifth European Turbulence Conf., Siena, Italy, 5 - 8 July 1994 (Ed. R Benzi) (Dordrecht: Kluwer Acad., 1995) p. 210
  11. Chen S et al. Phys. Rev. Lett. 79 2253 (1997)
  12. Dhruva B, Tsuji Y, Sreenivasan K R Phys. Rev. E 56 R4928 (1997)
  13. Grauer R, Homann H, Pinton J-F New J. Phys. 14 063016 (2012)
  14. The Clay Mathematics Institute (CMI): Millennium Problems, http://www.claymath.org/millennium-problems
  15. Lions J L Quelques Méthodes De Résolution Des Problèmes Aux Limites Non Linéarires (Paris: Dunod, 1969)
  16. Mattingly J C, Sinai Ya G Commun. Contemp. Math. 1 497 (1999)
  17. Zakharov V E, L’vov V S, Falkovich G Kolmogorov Spectra Of Turbulence I. Wave Turbulence (Berlin: Springer, 1992)
  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. Orlandi P, Pirozzoli S, Carnevale G F J. Fluid Mech. 690 288 (2012)
  20. Gibbon J D et al. Nonlinearity 27 2605 (2014)
  21. Okamoto N et al. Phys. Fluids 19 115109 (2007)
  22. Kopiev V, Chernyshev S Int. J. Aeroacoustics 13 39 (2014)
  23. Brachet M E et al. Phys. Fluids A 4 2845 (1992)
  24. She Z-S, Jackson E, Orszag S A Proc. R. Soc. Lond. A 434 101 (1991)
  25. Farge M, Pellegrino G, Schneider K Phys. Rev. Lett. 87 054501 (2001)
  26. Cafarelli L, Kohn R, Nirenberg L Commun. Pure Appl. Math. 35 771 (1982)
  27. Constantin P New Perspectives In Turbulence (Ed. L Sirovich) (New York: Springer-Verlag, 1991) p. 229
  28. Frisch U Chaotic Behavior of Deterministic Systems, Les Houches, Session XXXV, 1981 (Eds G Iooss, R H G Helleman, R Stora) (Amsterdam: North-Holland Publ. Co., 1983) p. 665
  29. Yakhot V, Orszag S A Phys. Rev. Lett. 57 1722 (1986)
  30. Eyink G, Goldenfeld N Phys. Rev. E 50 4679 (1994)
  31. Belinicher V I, L’vov V S Zh. Eksp. Teor. Fiz. 93 533 (1987); Belinicher V I, L’vov V S Sov. Phys. JETP 66 303 (1987)
  32. Chertkov M et al. Phys. Rev. E 52 4924 (1995)
  33. Parisi G, Frisch U Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics (Proc. Intern. School of Physics "Enrico Fermi") Vol. 88 (Eds M Ghil, R Benzi, G Parisi) (Amsterdam: North-Holland, 1985) p. 84
  34. Boffetta G, Mazzino A, Vulpiani A J. Phys. A Math. Theor. 41 363001 (2008)
  35. Arnol’d V I, Varchenko A N, Gusein-zade S M Osobennosti Differentsiruemykh Otobrazhenii T. 1 Klassifikatsiya Kriticheskikh Tochek, Kaustik i Volnovykh Frontov (M.: Nauka, 1982); Arnold V I, Gusein-Zade S M, Varchenko A N Singularities Of Differentiable Maps Vol. 1 The Classification Of Critical Points, Caustics And Wave Fronts (Boston: Birkhäuser, 1985)
  36. Moffatt H K, Kida S, Ohkitani K J. Fluid Mech. 259 241 (1994)
  37. Chorin A J Commun. Math. Phys. 132 519 (1990)
  38. Chorin A J, Akao J H Physica D 52 403 (1991)
  39. She Z-S, Leveque E Phys. Rev. Lett. 72 336 (1994)
  40. Zybin K P, Sirota V A, Il’in A S, Gurevich A V Zh. Eksp. Teor. Fiz. 132 510 (2007); Zybin K P, Sirota V A, Ilyin A S, Gurevich A V JETP 105 455 (2007)
  41. Zybin K P, Sirota V A, Ilyin A S, Gurevich A V Phys. Rev. Lett. 100 174504 (2008)
  42. Zybin K P, Sirota V A, Ilyin A S Phys. Rev. E 82 056324 (2010)
  43. Zybin K P, Sirota V A Phys. Rev. E 88 043017 (2013)
  44. de Karman T, Howarth L Proc. R. Soc. Lond. A 164 192 (1938)
  45. Falkovich G, Gawedzki K, Vergassola M Rev. Mod. Phys. 73 913 (2001)
  46. Balkovsky E, Lebedev V Phys. Rev. E 58 5776 (1998)
  47. Falkovich G, Lebedev V Phys. Rev. E 50 3883 (1994)
  48. Gamba A, Kolokolov I V J. Stat. Phys. 85 489 (1996)
  49. Letchikov A V Usp. Mat. Nauk 51 (1) 51 (1996); Letchikov A V Russ. Math. Surv. 51 49 (1996)
  50. Furstenberg H Trans. Am. Math. Soc. 108 377 (1963)
  51. Tutubalin V N Teoriya Veroyatn. Ee Primen. 10 19 (1965); Tutubalin V N Theory Probab. Appl. 10 15 (1965)
  52. Tutubalin V N Teoriya Veroyatn. Ee Primen. 22 209 (1977); Tutubalin V N Theory Probab. Appl. 22 203 (1978)
  53. Tutubalin V N Teoriya Veroyatn. Ee Primen. 14 319 (1969); Tutubalin V N Theory Probab. Appl. 14 313 (1969)
  54. Tutubalin V N Teoriya Veroyatn. Ee Primen. 13 63 (1968); Tutubalin V N Theory Probab. Appl. 13 65 (1968)
  55. Hill R J J. Fluid Mech. 434 379 (2001); Hill R J physics/0102063
  56. Il’yn A S, Zybin K P Phys. Lett. A 379 650 (2015)
  57. L’vov V S, Pomyalov A, Procaccia I Phys. Rev. E 63 056118 (2001)
  58. Balkovsky E, Fouxon A Phys. Rev. E 60 4164 (1999)
  59. Yakhot V Phys. Rev. E 63 026307 (2001)
  60. Biferale L, Procaccia I Phys. Rep. 414 43 (2005)
  61. Zhou T, Antonia R A J. Fluid Mech. 406 81 (2000)
  62. Schumacher J, Sreenivasan K R, Yakhot V New J. Phys. 9 89 (2007)
  63. Sirota V A, Zybin K P Phys. Scripta (T155) 014005 (2013); Zybin K P, Sirota V A arXiv:1204.1465
  64. Yakhot V J. Fluid Mech. 495 135 (2003)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions