Orthonormal Divergence-Free Wavelet Analysis of Spatial Correlation between Kinetic Energy and Nonlinear Transfer in Turbulence

  • Keiji Kishida
  • Keisuke Araki
Conference paper


Helical Meyer wavelet, an orthonormal divergence-free vector wavelet basis[1] is applied to the analysis of direct numerical simulation (DNS) data of incompressible isotropic turbulence. In the present study we focus our analysis on the correlation between the scale-location wavelet energy spectrum and nonlinear energy transfers relevant to its dynamics. Since helical Meyer wavelets are orthonormal and solenoidal, we can evaluate precisely the magnitude of nonlinear energy transfer between the wavelet modes with retaining the detailed energy balance. It is found that the magnitude of scale-location energy spectrum is positively correlated to those of relevant nonlinear energy transfers, i.e. nonlinear energy transfer actively occurs mainly in such domains that the fluid motions of assigned scale are intense. Batchelor and Townsend conjectured that intermittency of energy distribution in small scales may persist if the amount of energy transferred from a certain scale to smaller scales is determined by the energy density on the spot[2]. Our observation supports that such hypothetical process actually occurs as a result of the Navier-Stokes dynamics.


Energy Spectrum Direct Numerical Simulation Wavelet Analysis Coherent Structure Fluid Motion 
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  1. 1.
    Kishida, K., Araki, K., Suzuki, K., Kishiba, S., “Local or Nonlocal? Orthonormal divergence-free wavelet analysis of nonlinear interactions in turbulence” , Phys. Rev. Lett., 83, pp.5487–5490 (1999).CrossRefGoogle Scholar
  2. 2.
    Batchelor, G. K., and Townsend, A. A., “The nature of turbulent motion at large wave-numbers”, Proc. Roy. Soc. London, A199, pp.238–255 (1949).Google Scholar
  3. 3.
    Frisch U.. “Turbulence”, (Cambridge Univ. Press, Cambridge, 1995).MATHGoogle Scholar
  4. 4.
    Ohkitani, K., Kida, S., “Triad interactions in a forced turbulence” , Phys. Fluids A 4, pp. 794–802 (1992) .MATHCrossRefGoogle Scholar
  5. 5.
    Waleffe, F., “The nature of triad interactions in homogeneous turbulence”, Phys. Fluids A 4, pp.350–363 (1992).MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Kishida, K., Doctor thesis, (Hiroshima Univ., Hiroshima, 2000).Google Scholar
  7. 7.
    Arnold, V. I., “Mathematical method of classical mechanics” 2nd Ed., (Springer, New York. 1989).CrossRefGoogle Scholar
  8. 8.
    Kishiba, S., Ohkitani, K., Kida, S., “Physical-Space Nonlocality in Decaying Isotropic Turbulence”, J. Phys. Soc. Jpn., 62, pp.3783–3787 (1993).CrossRefGoogle Scholar
  9. 9.
    Iima, M., Toh, S., “Wavelet analysis of the energy transfer caused by convective terms: application to the Burgers shock” , Phys. Rev. E, 52, pp.6189–6201 (1995) .CrossRefGoogle Scholar

Copyright information

© Springer Japan 2003

Authors and Affiliations

  • Keiji Kishida
    • 1
  • Keisuke Araki
    • 2
  1. 1.Research Organization of Science and EngineeringRitsumeikan Univ.Japan
  2. 2.Dept. Assistive and Rehabilitation EngineeringOkayama Univ. Sci.Japan

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