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Reviews of topical problems


Quasi-two-dimensional turbulence

 a,  b
a A M Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Pyzhevskii per. 3, Moscow, 109017, Russian Federation
b Department of Mathematics, Case Western Reserve University, Cleveland, Ohio, USA

We review the results of numerical and experimental studies in quasi-two-dimensional (Q2D) turbulence. We demonstrate that theoretical energy spectra with slopes-5/3 and-3 (Kraichnan-Batchelor-Leith) can be observed only for a special set of external parameters. The bottom drag, beta effect, finite Rossby-Obukhov radius or vertical stratification, which distinguish geophysical Q2D turbulence from its purely 2D counterpart, determine the organization of a Q2D flow on a large scale. Since the spectral energy flux in 2D turbulence is directed upscale, the bottom friction takes on a special role. In the absence of bottom drag the energy condenses on the largest resolvable scale and flow equilibration is not attained.

Fulltext pdf (1.3 MB)
Fulltext is also available at DOI: 10.1070/PU2000v043n09ABEH000782
PACS: 47.27.Ak, 47.27.Eq, 92.10.−c, 92.90.+x (all)
DOI: 10.1070/PU2000v043n09ABEH000782
URL: https://ufn.ru/en/articles/2000/9/a/
000165206800001
Citation: Danilov S D, Gurarie D "Quasi-two-dimensional turbulence" Phys. Usp. 43 863–900 (2000)
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Оригинал: Данилов С Д, Гурарий Д «Квазидвумерная турбулентность» УФН 170 921–968 (2000); DOI: 10.3367/UFNr.0170.200009a.0921

References (156) ↓ Cited by (96) Similar articles (20)

  1. Kraichnan R H Phys. Fluids 10 1417 (1967)
  2. Kraichnan R H J. Fluid Mech. 47 525 (1971)
  3. Leith C E Phys. Fluids 11 671 (1968)
  4. Batchelor G K Phys. Fluids Suppl. II 12 233 (1969)
  5. Pedlosky J Geophysical Fluid Dynamics 2nd ed. (New York: Springer-Verlag, 1979) [Translated into Russian (Moscow: Mir, 1984)]
  6. Monin A S Theoretical Geophysical Fluid Dynamics (Dordrecht: Kluwer Academic Publishers, 1990)
  7. Salmon R Lectures on Geophysical Fluid Dynamics (New York: Oxford University Press, 1998)
  8. Rhines P B J. Fluid Mech. 69 417 (1975)
  9. Lilly D K Geophys. Fluid Dyn. 3 289 (1972)
  10. Manin D Yu Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 26 579 (1990)
  11. Danilov S D, Dolzhanskiî F V Izv. Ross. Akad. Nauk Fiz. Atmos. Okeana 34 (3) 293 (1998)
  12. Vallis G K, Maltrud M E J. Phys. Oceanogr. 23 1346 (1993)
  13. Panetta R L J. Atmos. Sci. 50 2073 (1993)
  14. Larichev V D, Held I M J. Phys. Oceanogr. 25 2285 (1995)
  15. Held I M, Larichev V D J. Atmos. Sci. 53 946 (1996)
  16. Monin A S, Mirabel’ A P Usp. Mekh. 2 (3) 47 (1979)
  17. Rhines P B Ann. Rev. Fluid Mech. 11 401 (1979)
  18. Mirabel’ A P, Monin A S Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 16 1011 (1980)
  19. Lesieur M Turbulence in Fluids 3d ed. (Dordrecht: Kluwer Acad. Publ., 1997)
  20. Vallis G K, in Nonlinear Phenomena in Atmospheric and Oceanic Sciences (The IMA Volumes in Mathematics and Its Applications, Vol. 40, Eds G F Carnevale, R T Pierrehumbert, New York: Springer-Verlag, 1992)
  21. 2D Turbulence. A Tentative Dictionary (NATO ASI Series. Ser. B: Physics, Vol. 341, Eds P Tabeling, O Cardoso, New York: Plenum Press, 1997)
  22. Monin A S, Ozmidov R V Okeanskaya Turbulentnost’ (Turbulence in the Ocean, Leningrad: Gidrometeoizdat, 1981) [Translated into English (Dordrecht: D.’Reidel Publ. Co., 1985)]
  23. Fjofort R Tellus 5 225 (1953)
  24. Novikov E L Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 14 668 (1978)
  25. Oetzel K G, Vallis G K Phys. Fluids 9 2991 (1997)
  26. Smith L M, Yakhot V Phys. Rev. Lett. 71 352 (1993)
  27. Smith L M, Yakhot V J. Fluid Mech. 274 115 (1994)
  28. Orszag S A J. Fluid Mech. 41 363 (1970)
  29. Holloway G Ann. Rev. Fluid Mech. 18 91 (1986)
  30. Paret J, Tabeling P Phys. Fluids 10 3126 (1998)
  31. Lindborg E J. Fluid Mech. 388 259 (1999)
  32. Babiano A, Dubrulle B, Frick P Phys. Rev. E 52 3719 (1995)
  33. Babiano A, Dubrulle B, Frick P Phys. Rev. E 55 2693 (1997)
  34. Landau L D, Lifshitz E M Fluid Mechanics (Oxford: Pergamon Press, 1959)
  35. Frisch U Turbulence: The Legacy of A N Kolmogorov (Cambridge: Cambridge University Press, 1995)
  36. Kolmogorov A N Dokl. Akad. Nauk SSSR 32 19 (1941)
  37. Kolmogorov A N Dokl. Akad. Nauk SSSR 30 299 (1941)
  38. Babiano A, Basdevant C, Sadourny R J. Atmos. Sci. 42 941 (1985)
  39. Lilly D K Phys. Fluids Suppl. II 12 240 (1969)
  40. Lilly D K J. Fluid Mech. 45 395 (1971)
  41. Maltrud M E, Vallis G K J. Fluid Mech. 228 321 (1991)
  42. Cho J Y-K, Polvani L M Phys. Fluids 8 1531 (1996)
  43. Maltrud M E, Vallis G K Phys. Fluids A 5 1760 (1993)
  44. Borue V Phys. Rev. Lett. 72 1475 (1994)
  45. Kukharkin N N J. Sci. Comput. 10 409 (1995)
  46. Chekhlov A et al. Phys. Fluids 6 2548 (1994)
  47. Nozawa T, Yoden S Phys. Fluids 9 2081 (1997)
  48. Borue V Phys. Rev. Lett. 71 3967 (1993)
  49. Chekhlov A et al. Physica D 98 321 (1996)
  50. Chasnov R J Phys. Fluids 9 171 (1997)
  51. Legras B, Santangelo P, Benzi R Europhys. Lett. 5 37 (1988)
  52. Ohkitani K Phys. Fluids A 3 1598 (1991)
  53. Ohkitani K Phys. Fluids A 2 1529 (1990)
  54. McWilliams J C J. Fluid Mech. 146 21 (1984)
  55. Herring J, McWilliams J J. Fluid Mech. 153 229 (1985)
  56. McWilliams J C Phys. Fluids A 2 547 (1990)
  57. Lesieur M, Herring J R J. Fluid Mech. 161 77 (1985)
  58. Dubrulle B, Nazarenko S Physica D 110 123 (1997)
  59. Gotoh T Phys. Rev. E 57 2984 (1998)
  60. Lindborg E, Avelius K Phys. Fluids 12 945 (2000)
  61. Frish U, Sulem P L Phys. Fluids 8 1921 (1984)
  62. Sukoriansky S, Galperin B, Chekhlov A Fhys. Fluids 11 3043 (1999)
  63. Yakhot V Phys. Rev. E 60 5544 (1999)
  64. Boffetta G, Celani A, Vergassola M Phys. Rev. E 61 R29 (2000)
  65. Fornberg B J. Comput. Phys. 25 1 (1977)
  66. Basdevant C et al. J. Atmos. Sci. 38 2305 (1981)
  67. Santangelo P, Benzi R, Legras B Phys. Fluids A 1 1027 (1989)
  68. Benzi R, Patarnello S, Santangelo P J. Phys. A 21 1221 (1988)
  69. McWilliams J C J. Fluid Mech. 219 361 (1990)
  70. Carnevale G F et al. Phys. Rev. Lett. 66 2735 (1991)
  71. Benzi R et al. Phys. Fluids A 4 1036 (1992)
  72. Weiss J B, McWilliams J C Phys. Fluids A 5 608 (1993)
  73. Matthaeus W H et al. Phys. Rev. Lett. 66 2731 (1991)
  74. Matthaeus W H et al. Physica D 51 531 (1991)
  75. Carnevale G F et al. Phys. Fluids A 4 1314 (1992)
  76. Dritschel D G Phys. Fluids A 5 984 (1993)
  77. Legras B, Dritschel D J. Comput. Phys. 104 287 (1993)
  78. Mariotti A, Legras B, Dritschel D G Phys. Fluids 6 3954 (1994)
  79. Bartello P, Warn T J. Fluid Mech. 326 357 (1996)
  80. Chasnov J R, Herring J R Phys. Fluids(in press)
  81. Dolzhansky F V Izv. Ross. Akad. Nauk Fiz. Atmos. Okeana 35 (2) 163 (1999) [Izv., Atm. Oceanic Phys. 35 147 (1999)]
  82. Dolzhanskiî F V, Krymov V A, Manin D Yu Usp. Fiz. Nauk 160 (7) 1 (1990) [Sov. Phys. Usp. 33 495 (1990)]
  83. Colin de Verdiere A Geophys. Astrophys. Fluid Dyn. 15 213 (1980)
  84. Sommeria J J. Fluid Mech. 170 139 (1986)
  85. Hopfinger E J, Griffiths R W, Mory M J. Mech. Theor. Appl. (Numéro Special) 2 21 (1983)
  86. Dolzhanskii F V, Manin D Yu Geophys. Astrophys. Fluid Dyn. 72 93 (1993)
  87. Danilov S D, Dolzhanskii F V, Krymov V A Chaos 4 (2) 299 (1994)
  88. Holloway G, Hendershott M J. Fluid Mech. 82 747 (1977)
  89. Kamenkovich V M, Koshlyakov M N, Monin A S Sinopticheskie Vikhri v Okeane (Synoptic Eddies in the Ocean, Leningrad: Gidrometeoizdat, 1982) [Translated into English (Dordtrecht: D. Reidel Publ. Co., 1986)]
  90. Williams G P J. Atmos. Sci. 35 1399 (1978)
  91. Huang H-P, Robinson W A J. Atmos. Sci. 55 611 (1998)
  92. Yoden S, Yamada M J. Atmos. Sci. 50 631 (1993)
  93. Larichev V D, McWilliams J C Phys. Fluids A 3 938 (1991)
  94. Kukharkin N, Orszag S A, Yakhot V Phys. Rev. Lett. 75 2486 (1995)
  95. Farge M, Sadorny R J. Fluid Mech. 206 433 (1989)
  96. McWilliams J C Phys. Fluids 10 3178 (1998)
  97. Yuan L, Hamilton K J. Fluid Mech. 280 369 (1994)
  98. Polvani L M et al. Chaos 4 (2) 177 (1994)
  99. Arai M, Yamagata T Chaos 4 163 (1994)
  100. Ford R Phys. Fluids 6 3694 (1993)
  101. Charney J G J. Atmos. Sci. 28 1087 (1971)
  102. Herring J R J. Atmos. Sci. 37 969 (1980)
  103. Hua B L, Haidvogel D B J. Atmos. Sci. 43 2923 (1986)
  104. McWilliams J C, Weiss J B Chaos 4 305 (1994)
  105. McWilliams J C J. Fluid Mech. 219 387 (1990)
  106. McWilliams J C, Weiss J B, Yavneh I J. Fluid Mech. 401 1 (1999)
  107. Gall R J. Atmos. Sci. 33 349 (1976)
  108. Randel W, Held I J. Atmos. Sci. 48 688 (1991)
  109. Olbers D, Wolf J-O, Völker C J. Phys. Oceanogr. 30 1645 (2000)
  110. Salmon R Geophys. Astrophys. Fluid Dyn. 10 25 (1978)
  111. Salmon R Geophys. Astrophys. Fluid Dyn. 15 167 (1980)
  112. McWilliams J C, Chow H S J. Phys. Oceanogr. 11 921 (1981)
  113. Held I M, O’Brien E J. Atmos. Sci. 49 1861 (1992)
  114. Haidvogel D B, Held I M J. Atmos. Sci. 37 2644 (1980)
  115. Whitaker J S, Barsilon A J. Atmos. Sci. 52 491 (1995)
  116. Lee S J. Atmos. Sci. 54 1726 (1997)
  117. Pavan V, Held I M J. Atmos. Sci. 53 1262 (1996)
  118. McWillliams J C Dyn. Atmos. Oceans 1 427 (1977)
  119. Nastrom G D, Gage K S J. Atmos. Sci. 42 950 (1985)
  120. Gage K S, Nastrom G D J. Atmos. Sci. 43 729 (1986)
  121. Högström U, Smedman A-S, Bergstróm H J. Atmos. Sci. 56 959 (1999)
  122. Wikle C K, Milliff R F, Large W G J. Atmos. Res. 56 2222 (1999)
  123. Larsen M F, Kellet M C, Gage K S J. Atmos. Sci. 39 1035 (1982)
  124. Lilly D K J. Atmos. Sci. 40 749 (1983)
  125. Lilly D K et al. Theor. Comput. Fluid Dyn. 11 139 (1998)
  126. Herring J R Fluid Dyn. Res. 24 363 (1999)
  127. Vallis G K, Shutts G J, Gray M E B Quart. J. R. Met. Soc. 12 1621 (1996)
  128. Lilly D K J. Atmos. Sci. 46 2026 (1989)
  129. Koshyk J N, Boer G J J. Atmos. Sci. 52 965 (1995)
  130. Straus D M, Ditlevsen P Tellus 51A 749 (1999)
  131. Tritton D J, in Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics (Proc. of the School of Physics "Enrico Fermi", Course 88, Eds M Ghil, R Benzi, G Parisi, Amsterdam: North-Holland, 1985) p. 172
  132. Hide R J. Fluid Mech. 32 737 (1968)
  133. Hide R, Mason P J Adv. Phys. 24 47 (1975)
  134. Couder Y, Chomaz J M, Rabaud M Physica D 37 384 (1989)
  135. Charib M, Derango P Physica D 37 406 (1989)
  136. Cardoso O, Marteau D, Tabeling P Phys. Rev. E 49 454 (1994)
  137. Marteau D, Cardoso O, Tabeling P Phys. Rev. E 51 5124 (1995)
  138. Hansen A E, Marteau D, Tabeling P Phys. Rev. E 58 7261 (1998)
  139. Kellay H, Wu X L, Goldburg W I Phys. Rev. Lett. 74 3975 (1995)
  140. Martin B K, Wu X L, Goldburg W I Phys. Rev. Lett. 80 3964 (1998)
  141. Rivera M, Vorobieff P, Recke R E Phys. Rev. Lett. 81 1417 (1998)
  142. Belmonte A et al. Phys. Fluids 11 1196 (1999)
  143. Kellay H, Bruneau C H, Wu X L Phys. Rev. Lett. 84 1696 (2000)
  144. Narimousa S, Maxworthy T, Spedding G R J. Fluid Mech. 223 113 (1991)
  145. Linden P F, Boubnov B M, Dalziel S B J. Fluid Mech. 298 81 (1995)
  146. Bastin M E, Read P L J. Fluid Mech. 339 173 (1997)
  147. Bastin M E, Read P L Phys. Fluids 10 374 (1998)
  148. Paret J, Tabeling P Phys. Rev. Lett. 79 4162 (1997)
  149. Danilov S D, Dovzhenko V A, Krymov V A Izv. Ross. Akad. Nauk Fiz. Atmos. Okeana 36 284 (2000) [Izv., Atm. Oceanic Phys. 36 261 (2000)]
  150. Paret J, Jullien M-C, Tabeling P Phys. Rev. Lett. 83 3418 (1999)
  151. Rutgers M A Phys. Rev. Lett. 81 2244 (1998)
  152. Bruneau C H, Greffier O, Kellay H Phys. Rev. E 60 1162 (1999)
  153. Salmon R, Holloway G, Hendershott M J. Fluid Mech. 75 691 (1976)
  154. Rober R, Sommeria J J. Fluid Mech. 229 291 (1991)
  155. Van de Konijenberg J A, Flór J D, Van Heijst G J F Phys. Fluids 10 595 (1998)
  156. Cardoso O et al. Phys. Fluids 8 209 (1996)
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