Wavelet transforms of the Navier-Stokes equations and the generalized dimensions of turbulence

Jacques Lewalle

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

The generalized dimensions Dqdefined in the multifractal description of turbulence are related to the Navier-Stokes equations, and equations are presented for Dqand 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.

Original languageEnglish (US)
Pages (from-to)109-113
Number of pages5
JournalApplied Scientific Research
Volume51
Issue number1-2
DOIs
StatePublished - Jun 1993

Keywords

  • Navier-Stokes
  • multifractals
  • wavelets

ASJC Scopus subject areas

  • Engineering(all)

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