Experimental assessment of fractal scale similarity in turbulent flows. Part 4. Effects of Reynolds and Schmidt numbers

Richard D. Frederiksen, Werner J.A. Dahm, David R. Dowling

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Experimental results are presented for the influence of Reynolds number on multifractal scale similarity in turbulent flows. These are obtained from single-point measurements of a dynamically passive Sc ≈ 1 conserved scalar quantity ζ(t) in a turbulent shear flow at outer-scale Reynolds numbers of 14000 ≤ Reδ 110000. Statistical criteria based on the maximum allowable scale-to-scale variation L1(ε) in multiplier distributions P(Mε) from multifractal gauge sets allow accurate discrimination between multifractal and non-multifractal scaling. Results show that the surrogate scalar energy dissipation rate χs(t) ≡ (dζ/dt)2 is found to display a scale-invariant similarity consistent with a random multiplicative cascade characterized by a bilinear multiplier distribution P(Mε) over a range of scales extending downward from the outer scale Tδ. For a range of scales extending upward from the inner (diffusive) scale TD, the dissipation rate displays a different scale-invariant similarity characterized by a uniform multiplier distribution. The former scale-invariance becomes evident in the present Sc ≈ 1 data only when Reδ is sufficiently large. Comparisons with results from Sc ≫ 1 data indicate that this scale-invariant similarity applies when the outer-to-inner scale ratio Tδ/TD ≈ 0.09 Reδ3/4 is greater than about 400. In contrast to the scalar dissipation rate field, the scalar field is found to lack any multifractal scale similarity.

Original languageEnglish (US)
Pages (from-to)169-187
Number of pages19
Journaljournal of fluid mechanics
StatePublished - Dec 25 1998
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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