- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Reviews of Modern Physics

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Fluid turbulence

Katepalli R. Sreenivasan

Katepalli R. Sreenivasan

  • Mason Laboratory, Yale University, New Haven, Connecticut 06520-8286

PDF

Rev. Mod. Phys. 71, S383 – Published 1 March, 1999

DOI: https://doi.org/10.1103/RevModPhys.71.S383

Abstract

The swirling motion of fluids that occurs irregularly in space and time is called turbulence. However, this randomness, apparent from a casual observation, is not without some order. Turbulent flows are as abundant in nature as life itself, and are pervasive in technology. They are a paradigm for spatially extended nonlinear dissipative systems in which many length scales are excited simultaneously and coupled strongly. The phenomenon has been studied extensively in engineering and in diverse fields such as astrophysics, oceanography, and meteorology. A few aspects of turbulence research in this century are briefly reviewed, and a partial assessment is made of the present directions.

View figure in article

References (134)

  1. Adrian, R.J., 1991, Annu. Rev. Fluid Mech. 23, 261.
  2. Arneodo, A., et al., 1996, Europhys. Lett. 34, 411.
  3. Anselmet, F., Y. Gagne, E.J. Hopfinger, and R.A. Antonia, 1983J. Fluid Mech. 140, 63.
  4. Avellaneda, M., and A.J. Majda, 1994, Philos. Trans. R. Soc. London, Ser. A 346, 205.
  5. Barenblatt, G.I., A.J. Chorin, and V.M. Prostokishin, 1997, Appl. Mech. Rev. 50, 413
  6. Barenblatt, G.I., and N. Goldenfeld, 1995, Phys. Fluids 7, 3078.
  7. Batchelor, G.K., 1953, The Theory of Homogeneous Turbulence (Cambridge University Press, England).
  8. Beale, J.T., T. Kato, and A.J. Majda, 1989, Commun. Math. Phys. 94, 61.
  9. Benzi, R., S. Ciliberto, R. Tripiccione, C. Baudet, F. Massaioli, and S. Succi, 1993, Phys. Rev. E 48, R29.
  10. Bonn, D., Y. Couder, P.H.J. van Damm, and S. Douady, 1993, Phys. Rev. E 47, R28.
  11. Bradshaw, P., 1971, An Introduction to Turbulence and Its Measurement (Pergamon, New York).
  12. Brown, G.L., and A. Roshko, 1974, J. Fluid Mech. 64, 775.
  13. Cafarelli, L., R. Kohn, and L. Nirenberg, 1982, Commun. Pure Apppl. Math. 35, 771.
  14. Cantwell, B.J., 1981, Annu. Rev. Fluid Mech. 13, 457.
  15. Canuto, V.M., and J. Christensen-Dalsgaard, 1998, Annu. Rev. Fluid Mech. 30, 167.
  16. Cao, N., S. Chen, and Z.-S. She, 1996, Phys. Rev. Lett. 76, 3714.
  17. Castaing, B., et al., 1989, J. Fluid Mech. 204, 1.
  18. Cheklov, A., and V. Yakhot, 1995, Phys. Rev. E 51, R2739.
  19. Chen, S., G.D. Doolen, R.H. Kraichnan, and Z.-S. She, 1993, Phys. Fluids A 5, 458.
  20. Chertkov, M., A. Pumir, and B.I. Shraiman, 1998, Phys. Fluids (submitted).
  21. Chorin, A.J., 1967, J. Comput. Phys. 2, 1.
  22. Chorin, A.J., 1994, Vorticity and Turbulence (Springer-Verlag, New York).
  23. Comte-Bellot, G., and S. Corrsin, 1966, J. Fluid Mech. 25, 657.
  24. Constantin, P., 1994, SIAM (Soc. Ind. Appl. Math.) Rev. 36, 73.
  25. Constantin, P., and C. Fefferman, 1994, Nonlinearity 7, 41.
  26. Constantin, P., I. Procaccia, and K.R. Sreenivasan, 1991, Phys. Rev. Lett. 67, 1739.
  27. Corrsin, S., 1963, in Handbuch der Physik, Fluid Dynamics II, edited by S. Flugge and C. Truesdell (Springer-Verlag, Berlin), p. 524.
  28. Cross, M.C., and P.C. Hohenberg, 1994, Rev. Mod. Phys. 65, 851.
  29. Dahm, W., K.B. Southerland, and K.A. Buch, 1991, Phys. Fluids A 3, 1115.
  30. Donnelly, R.J., 1991, Ed., High Reynolds Number Flows Using Liquid and Gaseous Helium (Springer-Verlag, New York).
  31. Drazin, P.G., and W.H. Reid, 1981, Hydrodynamic Stability (Cambridge University Press, England).
  32. Emmons, H.W., 1951, J. Aeronaut. Soc. 18, 490.
  33. Eyink, G., 1994, Phys. Fluids 6, 3063.
  34. Favre, A., J. Gaviglio, and R. Dumas, 1958, J. Fluid Mech. 3, 344.
  35. Forster, D., D.R. Nelson, and M.J. Stephen, 1977, Phys. Rev. A 16, 732.
  36. Frisch, U., 1995, Turbulence: The Legacy of A.N. Kolmogorov (Cambridge University Press, England)
  37. Frisch, U., and S.A. Orszag, 1990, Phase Transit. 43(1), 24.
  38. Frisch, V., A. Mazzino, and M. Vergassola, 1998, Phys. Rev. Lett. 80, 5532.
  39. Gad-el-Hak, M., A. Pollard, and J.-P. Bonnet, 1998, Eds., Flow Control: Fundamentals and Practices (Springer-Verlag, New York).
  40. Gollub, J.P., and H.L. Swinney, 1975, Phys. Rev. Lett. 35, 927.
  41. Grant, H.L., R.W. Stewart, and A. Moilliet, 1962, J. Fluid Mech. 12, 241.
  42. Grossmann, S., and D. Lohse, 1994, Phys. Rev. E 50, 2784.
  43. Halsey, T.C., M.H. Jensen, L.P. Kadanoff, I. Procaccia, and B.I. Shraiman, 1986, Phys. Rev. A 33, 1141.
  44. Head, M.R., and P. Bandyopadhyay, 1981, J. Fluid Mech. 107, 297.
  45. Heisenberg, W., 1948, Z. Phys. 124, 628.
  46. Holmes, P., J.L. Lumley, and G. Berkooz, 1998, Turbulence, Coherent Structures, Dynamical Systems and Symmetry (Cambridge University Press, England).
  47. Hussain, A.K.M.F., 1983, Phys. Fluids 26, 2816.
  48. Jensen, M.H., G. Paladin, and A. Vulpiani, 1991, Phys. Rev. A 43, 798.
  49. Jimenez, J., A.A. Wray, P.G. Saffman, and R.S Rogallo, 1993, J. Fluid Mech. 255, 65.
  50. Keller, L.V., and A. Friedmann, 1924, in Proceedings of the First International Congress on Applied Mechanics, edited by C.B. Biezeno and J.M. Burgers (Technische Boekhandel en drukkerij, J. Waltman, Jr., Delft), p. 395.
  51. Kida, S., and M. Takaoka, 1994, Annu. Rev. Fluid Mech. 26, 169.
  52. Kline, S.J., W.C. Reynolds, F.A. Schraub, and P.W. Runstadler, 1967, J. Fluid Mech. 30, 741.
  53. Kolmogorov, A.N., 1941a, Dokl. Akad. Nauk SSSR 32, 19.
  54. Kolmogorov, A.N., 1941b, Dokl. Akad. Nauk SSSR 30, 299.
  55. Kolmogorov, A.N., 1942, Izv. Akad. Nauk SSSR, Ser. Fiz. VI (1-2), 56.
  56. Kolmogorov, A.N., 1962, J. Fluid Mech. 13, 82.
  57. Kovasznay, L.S.G., V. Kibens, and R.F. Blackwelder, 1970, J. Fluid Mech. 41, 283.
  58. Kraichnan, R.H., 1959, J. Fluid Mech. 5, 497.
  59. Kraichnan, R.H., 1974, J. Fluid Mech. 62, 305.
  60. Kraichnan, R.H., 1994, Phys. Rev. Lett. 72, 1016.
  61. Landau, L.D., and E.M. Lifshitz, 1959, Fluid Mechanics (Pergamon, Oxford).
  62. Leonard, A., 1985, Annu. Rev. Fluid Mech. 17, 523.
  63. Lesieur, M., 1990, Turbulence in Fluids (Kluwer, Dordrecht).
  64. Lesieur, M., and O. Metais, 1996, Annu. Rev. Fluid Mech. 28, 45.
  65. Leslie, D.C. 1972, Developments in the Theory of Turbulence (Clarendon, Oxford).
  66. Liepmann, H.W., 1952, Z. Angew. Math. Phys. 3, 321.
  67. Liepmann, H.W., 1979, Am. Sci. 67, 221.
  68. Lumley, J.L., 1965, Phys. Fluids 8, 1056.
  69. Lumley, J.L., 1990, Ed., Whither Turbulence? Turbulence at the Crossroads (Springer-Verlag, New York).
  70. L’vov, V., and I. Procaccia, 1995, Phys. Rev. Lett. 74, 2690.
  71. L’vov, V., and I. Procaccia, 1996, Phys. World 9, 35.
  72. Majda, A., 1993, J. Stat. Phys. 73, 515.
  73. Malkus, W.V.R., 1956, J. Fluid Mech. 1, 521.
  74. Mandelbrot, B.B., 1974, J. Fluid Mech. 62, 331.
  75. Mandelbrot, B.B., 1982, The Fractal Geometry of Nature (Freeman, San Francisco).
  76. Martin, P.C., E.D. Siggia, and H.A. Rose, 1973, Phys. Rev. A 8, 423.
  77. McComb, W.D., 1990, The Physics of Fluid Turbulence (Oxford University Press, England).
  78. Meneveau, C., and K.R. Sreenivasan, 1991, J. Fluid Mech. 224, 429.
  79. Millikan, C.B., 1939, Proceedings of the Fifth International Congress on Applied Mechanics, edited by J.P. Den Hartog and H. Peters (John Wiley, New York), p. 386.
  80. Moffatt, H.K., 1994, J. Fluid Mech. 275, 406.
  81. Moffatt, H.K., S. Kida, and K. Ohkitani, 1994, J. Fluid Mech. 259, 241.
  82. Moin, P., 1996, in Research Trends in Fluid Mechanics, edited by J.L. Lumley, A. Acrivos, L.G. Leal, and S. Leibovich (AIP Press, New York), p. 188.
  83. Moin, P., and J. Kim, 1997, Sci. Am. 276, 62.
  84. Monin, A.S., and A.M. Yaglom, 1971, Statistical Fluid Mechanics (M.I.T. Press, Cambridge, MA), Vol. 1.
  85. Monin, A.S., A.M. Yaglom, 1975, Statistical Fluid Mechanics (MIT Press, Cambridge, MA) Vol. 2.
  86. Mou, C.-Y., and P. Weichman, 1995, Phys. Rev. E 52, 3738.
  87. Narasimha, R., 1983, J. Indian Inst. Sci. 64, 1.
  88. Narasimha, R., 1990, in Whither Turbulence? Turbulence at Cross Roads, edited by J.L. Lumley (Springer-Verlag, New York), p. 1.
  89. Nelkin, M., 1994, Adv. Phys. 43, 143.
  90. Novikov, E.A., 1990, Phys. Fluids A 2, 814.
  91. Onsager, L., 1945, Phys. Rev. 68, 286.
  92. Orszag, S.A., and G.S. Patterson, 1972, in Statistical Models and Turbulence, Lecture Notes in Physics, edited by M. Rosenblatt and C. W. Van Atta (Spring-Verlag, Berlin), Vol. 12, p. 127.
  93. Parisi, G., and U. Frisch, 1985, in Turbulence and Predictability in Geophysical Fluid Dynamics, edited by M. Ghil, R. Benzi, and G. Parisi (North Holland, Amsterdam), p. 84.
  94. Polyakov, A., 1995, Phys. Rev. E 52, 6183.
  95. Prandtl, L., 1925, Z. Angew. Math. Mech. 5, 136.
  96. Prandtl, L., and O.G. Tietjens, 1934, Applied Hydro- and Aeromechanics (Dover, New York).
  97. Reynolds, O., 1883, Philos. Trans. R. Soc. London 174, 935.
  98. Reynolds, O., 1894, Philos. Trans. R. Soc. London, Ser. A 186, 123.
  99. Reynolds, W.C., 1976, Annu. Rev. Fluid Mech. 8, 183.
  100. Richardson, L.F., 1922, Weather Prediction by Numerical Process (Cambridge University Press, England).
  101. Richardson, L.F., 1926, Proc. R. Soc. London, Ser. A A110, 709.
  102. Roshko, A., 1976, AIAA J. 14, 1349.
  103. Ruelle, D., and F. Takens, 1971, Commum. Math. Phys. 20, 167.
  104. Saffman, P.G., 1968, in Topics in Nonlinear Physics, edited by N.J. Zabusky (Springer, Berlin), p. 485.
  105. Saffman, P.G., 1992, Vortex Dynamics (Cambridge Univeristy Press, England)
  106. Schlichting, H., 1956, Boundary Layer Theory (McGraw Hill, New York).
  107. She, Z.-S., E. Jackson, and S.A. Orszag, 1990, Nature (London) 344, 226.
  108. She, Z.-S., and E. Leveque, 1994. Phys. Rev. Lett. 72, 336.
  109. Shraiman, B., and E.D. Siggia, 1995, C.R. Acad. Sci. Ser. IIb: Mec., Phys., Chim., Astron. 321, 279.
  110. Siggia, E.D., 1994, Annu. Rev. Fluid Mech. 26, 137.
  111. Sirovich, L., 1987, Quart. Appl. Math. 45, 561.
  112. Smith, L.M., and S.L. Woodruff, Annu. Rev. Fluid Mech. 30, 275.
  113. Speziale, C.G., 1991, Annu. Rev. Fluid Mech. 23, 107.
  114. Sreenivasan, K.R., 1991, Proc. R. Soc. London, Ser. A 434, 165.
  115. Sreenivasan, K.R., and R.A. Antonia, 1997, Annu. Rev. Fluid Mech. 29, 435.
  116. Sreenivasan, K.R., and B. Dhruva, 1998, Prog. Theor. Phys. Suppl. 130, 103.
  117. Stolovitzky, G., and K.R. Sreenivasan, 1994, Rev. Mod. Phys. 66, 229.
  118. Tabeling, P., G. Zocchi, F. Belin, J. Maurer, and J. Williame, 1996, Phys. Rev. E 53, 1613.
  119. Taylor, G.I., 1915, Philos. Trans. R. Soc. London, Ser. A 215, 1.
  120. Taylor, G.I., 1932, Proc. R. Soc. London, Ser. A 135, 685.
  121. Taylor, G.I., 1935, Proc. R. Soc. London, Ser. A 151, 421.
  122. Taylor, G.I., 1938, Proc. R. Soc. London, Ser. A 164, 15,476.
  123. Tennekes, H., and J.L. Lumley, 1972, A First Course in Turbulence (MIT Press, Cambridge, MA).
  124. Townsend, A.A., 1956, The Structure of Turbulent Shear Flow (Cambridge University Press, England).
  125. Van Dyke, M., 1982, An Album of Fluid Motion (Parabolic Press, Stanford).
  126. von Kármán, T., 1930, Nachr. Ges. Wiss. Goettingen, Math. Phys. K1, 58.
  127. von Kármán, T., 1937, J. Aeronaut. Sci. 4, 131.
  128. von Kármán, T., and L. Howarth, 1938, Proc. R. Soc. London, Ser. A 164, 192.
  129. von Weizsäcker, C.F., 1948, Z. Phys. 124, 614.
  130. Wygnanski, I.J., F.H. Champagne, and B. Marasli, 1986, J. Fluid Mech. 168, 31.
  131. Yakhot, V., and S.A. Orszag, 1986, Phys. Rev. Lett. 57, 1722.
  132. Zabusky, N.J., and M. D. Kruskal, 1965, Phys. Rev. Lett. 15, 240.
  133. Zagaraola, M., and A.J. Smits, 1996, Phys. Rev. Lett. 78, 239.
  134. Zhou, Y., and C.G. Speziale, 1998, Appl. Mech. Rev. 1, 267.

Outline

Information

Rev. Mod. Phys. 71, S383– Published 1 March, 1999

    © 1999 American Physical Society

    Sign In to Your Journals Account

    Filter

    Filter

    Article Lookup

    Enter a citation