On the Decay of Isotropic Turbulence

  • P. A. Davidson
  • Y. Kaneda
  • T. Ishida
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 109)


We investigate the decay of freely-evolving, isotropic turbulence whose spectrum takes the form E(k→0)∼Ik4, I being Loitsyansky's integral. We report numerical simulations in a periodic domain whose dimensions, lbox, are much larger than the integral scale of the turbulence, l. We find that, provided lbox≫l and Re≫1, the turbulence evolves to a state in which Loitsyansky's integral is approximately constant and Kolmogorov's decay law, u2∼t−10/7, holds true. The approximate conservation of I in fully-developed turbulence implies that the long-range interactions between remote eddies, as measured by the triple correlations, are very weak.


Direct Numerical Simulation Integral Scale Isotropic Turbulence Traditional Theory Periodic Domain 
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  1. 1.
    Landau L D, Lifshitz E M (1959) Fluid Mechanics, 1st Edn., PergamonGoogle Scholar
  2. 2.
    Kolmogorov A N (1941) Dokl. Akad. Nauk SSSR, 31(6), 538-541Google Scholar
  3. 3.
    Saffman P G (1967) J. Fluid Mech., 27, 581-593.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Davidson P A (2000) Jn. of Turbulence, 1.Google Scholar
  5. 5.
    Davidson P A (2004) Turbulence: An Introduction for Scientists and Engineers, Oxford University Press.Google Scholar
  6. 6.
    Batchelor G K, Proudman I (1956) Phil. Trans. Roy. Soc. A, 248, 369-405.MathSciNetGoogle Scholar
  7. 7.
    Birkhoff G (1954) Commun. Pure & Applied Math., 7, 19-44.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Kaneda Y, Ishihara T (2004). In: Reynolds number scaling in turbulent flows. Edited by A J Smits, Kluwer Acad. Publishers, 155-162.Google Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • P. A. Davidson
    • 1
  • Y. Kaneda
    • 2
  • T. Ishida
    • 3
  1. 1.Dept. EngineeringUniversity of CambridgeCambridgeUK
  2. 2.Dept. Computational Science & EngineeringNagoya UniversityNagoyaJapan
  3. 3.Dept. Computational Science & EngineeringNagoya UniversityNagoyaJapan

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