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

Issues

 / 

2022

 / 

February

←  →

Methodological notes


Compressible vortex structures and their role in the onset of hydrodynamic turbulence

†  a, b, ‡  c, d, b, §  e, *  b, f
a P.P. Shirshov Institute of Oceanology, Russian Academy of Sciences, ul. Krasikova 23, Moscow, 117218, Russian Federation
b Skolkovo Institute of Science and Technology, Bolshoy Boulevard 30, bld. 1, Moscow, 121205, Russian Federation
c Lebedev Physical Institute, Russian Academy of Sciences, Leninsky prosp. 53, Moscow, 119991, Russian Federation
d Landau Institute for Theoretical Physics, Russian Academy of Sciences, ul. Kosygina 2, Moscow, 119334, Russian Federation
e Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, CEP 22460-320, Brasil
f Khristianovich Institute of Theoretical and Applied Mechanics SB RAS, Institutskaya str., 4/1, Novosibirsk, 630090, Russian Federation

We study the formation of quasi-two-dimensional (thin pancake) vortex structures in three-dimensional flows and of quasi-one-dimensional structures in two-dimensional hydrodynamics. These structures are formed at large Reynolds numbers, when their evolution is described in the leading order by the Euler equations for an ideal incompressible fluid. We show numerically and analytically that the compression of these structures and, as a consequence, the increase in their amplitudes are due to the compressibility of the frozen-in-fluid fields: the field of continuously distributed vortex lines in the three-dimensional case and the field of vorticity rotor lines (divorticity) for two-dimensional flows. We find that the growth of vorticity and divorticity can be considered to be a process of overturning the corresponding fields. At high intensities, this process demonstrates a Kolmogorov-type scaling relating the maximum amplitude to the corresponding thicknesses-to-width ratio of the structures. The possible role of these coherent structures in the formation of the Kolmogorov turbulent spectrum, as well as in the Kraichnan spectrum corresponding to a constant flux of enstrophy in the case of two-dimensional turbulence, is analyzed.

Fulltext pdf (1.1 MB)
Fulltext is also available at DOI: 10.3367/UFNe.2020.11.038875
Keywords: vortex lines, divorticity, overturning, turbulence, frozen-in-fluid fields
PACS: 47.10.−g, 47.27.−i, 47.32.−y (all)
DOI: 10.3367/UFNe.2020.11.038875
URL: https://ufn.ru/en/articles/2022/2/d/
000805351300005
2-s2.0-85129834016
2022PhyU...65..189A
Citation: Agafontsev D S, Kuznetsov E A, Mailybaev A A, Sereshchenko E V "Compressible vortex structures and their role in the onset of hydrodynamic turbulence" Phys. Usp. 65 189–208 (2022)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 31st, August 2020, 18th, November 2020

Оригинал: Агафонцев Д С, Кузнецов Е А, Майлыбаев А А, Серещенко Е В «Сжимаемые вихревые структуры и их роль в зарождении гидродинамической турбулентности» УФН 192 205–225 (2022); DOI: 10.3367/UFNr.2020.11.038875

References (75) ↓ Cited by (3) Similar articles (20)

  1. Richardson L F Proc. R. Soc. Lond. A 110 709 (1926)
  2. Kolmogorov A N Dokl. Akad. Nauk SSSR 30 299 (1941); Per. na angl. yaz., Kolmogorov A N Proc. R. Soc. Lond. A 434 9 (1991)
  3. Obukhov A M Dokl. Akad. Nauk SSSR 32 22 (1941)
  4. Zakharov V E, L’vov V S, Falkovich G Kolmogorov Spectra Of Turbulence. I Wave Turbulence (Berlin: Springer, 1992)
  5. Zakharov V E Stud. Appl. Math. 122 219 (2009)
  6. Suret P, Picozzi A, Randoux S Opt. Exp. 19 17852 (2011)
  7. Picozzi A at al. Phys. Rep. 542 1 (2014)
  8. Walczak P, Randoux S, Suret P Phys. Rev. Lett. 114 143903 (2015)
  9. Agafontsev D S, Zakharov V E Nonlinearity 28 2791 (2015)
  10. Agafontsev D S, Zakharov V E Nonlinearity 29 3551 (2016)
  11. Gelash A A, Agafontsev D S Phys. Rev. E 98 042210 (2018)
  12. Agafontsev D S, Randoux S, Suret P Phys. Rev. E 103 032209 (2021)
  13. Zakharov V E, Kuznetsov E A Usp. Fiz. Nauk 182 569 (2012); Zakharov V E, Kuznetsov E A Phys. Usp. 55 535 (2012)
  14. Zakharov V E, Kuznetsov E A Usp. Fiz. Nauk 167 1137 (1997); Zakharov V E, Kuznetsov E A Phys. Usp. 40 1087 (1997)
  15. Landau L D, Lifshits E M Gidrodinamika (M.: Nauka, 1986); Per. na angl. yaz., Landau L D, Lifshitz E M Fluid Mechanics (Oxford: Pergamon Press, 1987)
  16. Arnol’d V I Matematicheskie Metody Klassicheskoi Mekhaniki (M.: Nauka, 1979); Per. na angl. yaz., Arnold V I Mathematical Methods In Classical Mechanics (New York: Springer-Verlag, 1989)
  17. Kuznetsov E A, Mikhailov A V Phys. Lett. A 77 37 (1980)
  18. Moreau J J C.R. Hebdomadaires S 252 2810 (1961)
  19. Moffatt H K J. Fluid Mech. 35 117 (1969)
  20. Arnol’d V I Usp. Mat. Nauk 24 225 (1969)
  21. Kuznetsov E A Pis’ma ZhETF 76 406 (2002); Kuznetsov E A JETP Lett. 76 346 (2002)
  22. Yakubovich E I, Zenkovich D A Progress In Nonlinear Science: International Conference Dedicated To The 100th Anniversary Of A.A. Andronov Vol. 2 (Ed. A G Litvak) (Nizhny Novgorod: Inst. of Applied Physics, Univ. of Nizhny Novgorod, 2002) p. 282; Yakubovich E I, Zenkovich D A physics/0110004
  23. Frisch U, Villone B Eur. Phys. J. H 39 325 (2014)
  24. Kuznetsov E A, Ruban V P Pis’ma ZhETF 67 1015 (1998); Kuznetsov E A, Ruban V P JETP Lett. 67 1076 (1998)
  25. Kuznetsov E A, Ruban V P Zh. Eksp. Teor. Fiz. 118 893 (2000); Kuznetsov E A, Ruban V P JETP 91 775 (2000)
  26. Arnol’d V I Teoriya Katastrof (M.: Znanie, 1981); Per. na angl. yaz., Arnold V I Catastrophe Theory (Berlin: Springer-Verlag, 1984)
  27. Yakubovich E I, Zenkovich D A J. Fluid Mech. 443 167 (2001)
  28. Kuznetsov E A J. Nonlin. Math. Phys. 13 64 (2006)
  29. Brachet M E et al J. Fluid Mech. 194 333 (1988)
  30. Weiss J Physica D 48 273 (1991)
  31. Kuznetsov E A et al Phys. Fluids 19 105110 (2007)
  32. Hasimoto H J. Fluid Mech. 51 477 (1972)
  33. Zakharov V E, Takhtadzhyan L A Teor. Mat. Fiz. 38 26 (1972); Zakharov V E, Takhtadzhyan L A Theor. Math. Phys. 38 17 (1979)
  34. Chae D Handbook Of Differential Equations: Evolutionary Equations Vol. 4 (Eds C M Dafermos, M Pokorny) (Oxford: Elsevier, 2008) p. 1
  35. Gibbon J D Physica D 237 1894 (2008)
  36. Agafontsev D S, Kuznetsov E A, Mailybaev A A Phys. Fluids 27 085102 (2015)
  37. Agafontsev D S, Kuznetsov E A, Mailybaev A A Pis’ma ZhETF 104 695 (2016); Agafontsev D S, Kuznetsov E A, Mailybaev A A JETP Lett. 104 685 (2016)
  38. Agafontsev D S, Kuznetsov E A, Mailybaev A A J. Fluid Mech. 813 R1 (2017)
  39. Brachet M E et al Phys. Fluids A 4 2845 (1992)
  40. Agafontsev D S, Kuznetsov E A, Mailybaev A A Pis’ma ZhETF 110 106 (2019); Agafontsev D S, Kuznetsov E A, Mailybaev A A JETP Lett. 110 121 (2019)
  41. Kuznetsov E A, Passot T, Sulem P L Phys. Plasmas 11 1410 (2004)
  42. Kuznetsov E A J. Fluid Mech. 600 167 (2008)
  43. Shandarin S F, Zeldovich Ya B Rev. Mod. Phys. 61 185 (1989)
  44. Gurbatov S N, Saichev A I, Shandarin S F Usp. Fiz. Nauk 182 233 (2012); Gurbatov S N, Saichev A I, Shandarin S F Phys. Usp. 55 223 (2012)
  45. Kuznetsov E A, Sereshchenko E V Pis’ma ZhETF 102 760 (2015)
  46. Kuznetsov E A, Sereshchenko E V Pis’ma ZhETF 105 70 (2017); Kuznetsov E A, Sereshchenko E V JETP Lett. 105 83 (2017)
  47. Kudryavtsev A N, Kuznetsov E A, Sereshchenko E V Pis’ma ZhETF 96 783 (2012); Kudryavtsev A N, Kuznetsov E A, Sereshchenko E V JETP Lett. 96 699 (2012)
  48. Kuznetsov E A Nauchnaya shkola "Nelineinye volny 2016" Nizhnii Novgorod, 27 fevralya - 4 marta 2016, lektsiya; Agafontsev D S, Kuznetsov E A, Mailybaev A A Nelineinye Volny 2016 (Otv. red. A M Sergeev, A V Slyunyaev) (Nizhnii Novgorod: IPF RAN, 2017) p. 304
  49. Kuznetsov E A Nauchnaya shkola "Nelineinye volny 2018", Nizhnii Novgorod, 26 fevralya - 4 marta 2018, lektsiya; Kuznetsov E A i dr Nelineinye Volny 2018 (Otv. red. A G Litvak, A V Slyunyaev) (Nizhnii Novgorod: IPF RAN, 2019) p. 238
  50. Salmon R Annu. Rev. Fluid Mech. 20 225 (1988)
  51. Kuznetsov E A, Ruban V P Phys. Rev. E 61 831 (2000)
  52. Agafontsev D S, Kuznetsov E A, Mailybaev A A Phys. Fluids 30 095104 (2018)
  53. Frisch U Turbulence: The Legacy Of A.N. Kolmogorov (Cambridge: Cambridge Univ. Press, 1995); Per. na russk. yaz., Frish U Turbulentnost’. Nasledie A.N. Kolmogorova (M.: Fazis, 1998)
  54. Orlandi P, Pirozzoli S Theor. Comput. Fluid Dyn. 24 247 (2010)
  55. Holm D D, Kerr R M Phys. Rev. Lett. 88 244501 (2002)
  56. Cichowlas C et al Phys. Rev. Lett. 95 264502 (2005)
  57. Holm D D, Kerr R M Phys. Fluids 19 025101 (2007)
  58. Brachet M E et al Phys. Fluids A 4 2845 (1992)
  59. Ishihara T, Gotoh T, Kaneda Y Annu. Rev. Fluid Mech. 41 165 (2009)
  60. Gotoh T, Fukayama D, Nakano T Phys. Fluids 14 1065 (2002)
  61. Zybin K P, Sirota V A Usp. Fiz. Nauk 185 593 (2015); Zybin K P, Sirota V A Phys. Usp. 58 556 (2015)
  62. Kraichnan R H Phys. Fluids 10 1417 (1967)
  63. Boffetta G, Ecke R E Annu. Rev. Fluid Mech. 44 427 (2012)
  64. Lilly D K J. Fluid Mech. 45 395 (1971)
  65. Saffman P G Stud. Appl. Math. 50 377 (1971)
  66. Kadomtsev B B, Petviashvili V I Dokl. Akad. Nauk SSSR 208 794 (1973); Kadomtsev B B, Petviashvili V I Sov. Phys. Dokl. 18 115 (1973)
  67. Kuznetsov E A Pis’ma ZhETF 80 92 (2004); Kuznetsov E A JETP Lett. 80 83 (2004)
  68. Wolibner W Math. Z. 37 698 (1933)
  69. Kato T Arch. Rational Mech. Anal. 25 188 (1967)
  70. Yudovich V I Zhurn. Vychislitel’noi Matematiki Matematicheskoi Fiziki 3 1032 (1963); Yudovich V I USSR Comput. Math. Math. Phys. 3 01407 (1963)
  71. Kuznetsov E A et al Theor. Comput. Fluid Dyn. 24 253 (2010)
  72. Kuznetsov E A, Sereshchenko E V Pis’ma ZhETF 109 231 (2019); Kuznetsov E A, Sereshchenko E V JETP Lett. 109 239 (2019)
  73. Falkovich G, Lebedev V Phys. Rev. E 83 045301 (2011)
  74. Parker E N Astrophys. J. 138 552 (1963)
  75. Kuznetsov E A, Mikhailov E A Zh. Eksp. Teor. Fiz. 158 561 (2020); Kuznetsov E A, Mikhailov E A J. Exp. Theor. Phys. 131 496 (2020)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions