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Wavelet Transforms of the Navier-Stokes Equations and the Generalized Dimensions of Turbulence

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Advances in Turbulence IV

Part of the book series: Fluid Mechanics and its Applications ((FMIA,volume 18))

Abstract

The generalized dimensions D q defined in the multifractal description of turbulence are related to the Navier-Stokes equations, and equations are presented for D q and its evolution. In order to reach this result, the equations for incompressible flows are wavelet-transformed. When the analyzing wavelets belong in the Gaussian family, the pressure and momentum equations are transformed into first-order wave equations, for which the characteristics are obtained explicitly. Formal integration is carried out. As in Meneveau (1991), fractal statistics are then constructed from the local energy spectrum.

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References

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Author information

Authors and Affiliations

  1. Department of Mechanical, Aerospace and Manufacturing Engineering, Syracuse University, USA

    Jacques Lewalle

Authors
  1. Jacques Lewalle
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Editor information

Editors and Affiliations

  1. Laboratory for Aero- and Hydromechanics, Technical University of Delft, The Netherlands

    F. T. M. Nieuwstadt

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© 1993 Springer Science+Business Media Dordrecht

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Lewalle, J. (1993). Wavelet Transforms of the Navier-Stokes Equations and the Generalized Dimensions of Turbulence. In: Nieuwstadt, F.T.M. (eds) Advances in Turbulence IV. Fluid Mechanics and its Applications, vol 18. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1689-3_19

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  • DOI: https://doi.org/10.1007/978-94-011-1689-3_19

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4739-5

  • Online ISBN: 978-94-011-1689-3

  • eBook Packages: Springer Book Archive

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