Kinematics of Small Scale Motions in Homogeneous Isotropic Turbulence

  • J. C. R. Hunt
  • J. C. H. Fung
  • N. A. Malik
  • R. J. Perkins
  • J. C. Vassilicos
  • A. A. Wray
  • J. C. Buell
  • J. P. Bertoglio

Abstract

Using direct numerical simulation and ‘kinematic simulation’ (henceforth KS) of velocity fields, measurement, flow visualisation and novel kinematic analysis, the following aspects of small scale motions in turbulence were investigated: (i) Random advection and distortion of small scale motions by larger scale motions; (ii) the Lagrangian spectrum at high frequency of particles moving in small scale eddies and the effects of the time dependence of the eddies; (iii) the relative velocities Δu and the separation distance l between pairs of particles, to find the decorrelation time scales of Δu and the relation between the mean square separation \({\bar l^2}\) and the conditional displacements of single particles; (iv) how the forms of these motions can be inferred from the asymptotic forms of Fourier series and spectra; (v) the specific implications for Eulerian and Lagrangian spectra of the small scales being mostly associated with elongated regions of spiralling motions in which there are different orders of discontinuous derivatives of velocity normal to streamline surfaces. These studies suggest that small scale motion in isotropic turbulence has a characteristic spiralling structure, which is generally consistent with statistics, such as fractals, spectra and probability distributions.

Keywords

Vortex Covariance Helium Vorticity Advection 

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References

  1. Batchelor, G.K. 1952 Proc. Carnb. Phil. Soc., 48, 345–362.CrossRefMATHADSMathSciNetGoogle Scholar
  2. Batchelor, G.K. 1953 The theory of homogeneous turbulence. CUP, New York.MATHGoogle Scholar
  3. Bertoglio, J.P. 1986 These d’Etat, Universite C. Bernard, Lyon.Google Scholar
  4. Briscoli, M., Maggiore, P., Piccolo, F., Santongelo, P., Succi, S., Vitaletti, M., Zecca, V. 1989 ER­COFTAC Bulletin III, 3–7Google Scholar
  5. Chase, D.M. 1970 Acustica 22, 303–320.Google Scholar
  6. Courant & Hilbert 1953 Methods Of Mathemayical Physics Vol.1 Interscience, New York.Google Scholar
  7. Dritschel, D.G. 1989 Comput. Phys. Rep. 10(3), 77–146.CrossRefADSGoogle Scholar
  8. Favre, A.J., Gaviglio, J.J. & Dumas, R. 1957 J. Fluid Mech. 2, 313–342.CrossRefADSMathSciNetGoogle Scholar
  9. Fermigier, M. 1980 Ph.D. dissertation. L’Universite Pierre Et Marie Curie, Paris.Google Scholar
  10. Frisch, U. & Orszag, S. 1990 Physics Today 43(1), 24–32.CrossRefADSGoogle Scholar
  11. Fung, J.C.H. 1990 Ph.D. dissertation. University of Cambridge.Google Scholar
  12. Fung, J.C.H., Hunt, J.C.R., Malik, N.A. & Perkins, R.J. 1990 Submitted to J. Fluid Mech.Google Scholar
  13. Gilbert, A.D. 1988 J. Fluid Mech. 193, 475–497.CrossRefMATHADSMathSciNetGoogle Scholar
  14. Hanna, S.R. 1980 J. Appl. Meteor. 20, 242–249.CrossRefGoogle Scholar
  15. Hunt, J.C.R. & Carruthers, D.J. 1990 J. Fluid Mech. 212, 497–532.CrossRefMATHADSMathSciNetGoogle Scholar
  16. Hunt, J.C.R., Buell, J.C. & Wray, A.A. 1987 NASA Report CTR-S87.Google Scholar
  17. Inoue, E. 1951 On turbulent diffusion in the atmosphere. J. Met. Soc. Japan 29, 246–252.Google Scholar
  18. Lundgren, T.S. 1982 Phys. Fluids 25, 2193–2903.CrossRefMATHADSGoogle Scholar
  19. Malik, N.A. 1991 Ph.D. dissertation. University of Cambridge.Google Scholar
  20. McWilliams, J.C. 1984 J. Fluid Mech. 146, 21–43.CrossRefMATHADSGoogle Scholar
  21. Meneguzzi, M. 1990 In Advances In Turbulence 3 Springer Verlag.Google Scholar
  22. Moffatt, H.K. 1984 In ’Turbulence And Chaotic Phenomena In Fluids’, pp. 223–230 North-Holland.Google Scholar
  23. Monin, A.S. & Yagloin, A.M. 1975 Statistical Fluid Mechanics. Vol. 2, M.I.T. Press.Google Scholar
  24. Novikov, E.A. 1963 Soviet Phys. JETP 17, 1449–1453.MATHGoogle Scholar
  25. Obukhov, A. 1941 Bull. Acad. Sci. U.S.S.R., Geog. & Geophys., Moscow p453.Google Scholar
  26. Richardson, L.F. 1926 Proc. Roy. Soc., London, A. 110, 709–737.CrossRefADSGoogle Scholar
  27. Tatarski, V.I. 1960 Izv. Vyssh. Uchebn. Zaved., 3 Radiofizika 4, 551–583.Google Scholar
  28. Tennekes, H. 1975 J. Fluid Mech. 67, 561–567.CrossRefMATHADSGoogle Scholar
  29. Thomson, D.J. 1986 Quart. J. Roy. Met. Soc. 112, 890–894.CrossRefADSGoogle Scholar
  30. Thomson, D.J. 1989 In Advances In Turbulence. 2 Springer Verlag.Google Scholar
  31. Van Dop, H., Nieuwstadt, F.T.M. & Hunt, J.C.R. 1985 Phys. Fluid 28, 1693–1653.Google Scholar
  32. Vassilicos, J.C. 1989 In Advances In Turbulence. 2 Springer Verlag.Google Scholar
  33. Vassilicos, J.C. & Hunt, J.C.R. 1991 Submitted to Proc. Roy. Soc.Google Scholar
  34. Wray, A. & Hunt, J.C.R. 1990 In ’Topological Fluid Mechanics’, pp. 95–10.4. CUP.Google Scholar
  35. Yeung, P.K. & Pope, S.B. 1989 J. Fluid Mech. 207, 531–586.CrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin, Heidelberg 1991

Authors and Affiliations

  • J. C. R. Hunt
    • 1
  • J. C. H. Fung
    • 1
  • N. A. Malik
    • 1
  • R. J. Perkins
    • 1
  • J. C. Vassilicos
    • 1
  • A. A. Wray
    • 2
  • J. C. Buell
    • 2
  • J. P. Bertoglio
    • 3
  1. 1.DAMTPUniversity of CambridgeUK
  2. 2.NASA Ames Research CenterMoffett FieldUSA
  3. 3.Ecole Centrale de LyonEcullyFrance

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