Fractality and the law of the wall

Haosen H.A. Xu, X. I.A. Yang

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Fluid motions in the inertial range of isotropic turbulence are fractal, with their space-filling capacity slightly below regular three-dimensional objects, which is a consequence of the energy cascade. Besides the energy cascade, the other often encountered cascading process is the momentum cascade in wall-bounded flows. Despite the long-existing analogy between the two processes, many of the thoroughly investigated aspects of the energy cascade have so far received little attention in studies of the momentum counterpart, e.g., the possibility of the momentum-transferring scales in the logarithmic region being fractal has not been considered. In this work, this possibility is pursued, and we discuss one of its implications. Following the same dimensional arguments that lead to the D=2.33 fractal dimension of wrinkled surfaces in isotropic turbulence, we show that the large-scale momentum-carrying eddies may also be fractal and non-space-filling, which then leads to the power-law scaling of the mean velocity profile. The logarithmic law of the wall, on the other hand, corresponds to space-filling eddies, as suggested by Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1980)]. Because the space-filling capacity is an integral geometric quantity, the analysis presented in this work provides us with a low-order quantity, with which, one would be able to distinguish between the logarithmic law and the power law.

Original languageEnglish (US)
Article number053110
JournalPhysical Review E
Volume97
Issue number5
DOIs
StatePublished - May 29 2018

Fingerprint

Cascade
fractals
cascades
Momentum
momentum
Fractal
Logarithmic
isotropic turbulence
Turbulence
Power Law
Energy
vortices
wall flow
Shear Flow
Velocity Profile
Turbulent Flow
shear flow
Fractal Dimension
scaling laws
Analogy

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Xu, Haosen H.A. ; Yang, X. I.A. / Fractality and the law of the wall. In: Physical Review E. 2018 ; Vol. 97, No. 5.
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Fractality and the law of the wall. / Xu, Haosen H.A.; Yang, X. I.A.

In: Physical Review E, Vol. 97, No. 5, 053110, 29.05.2018.

Research output: Contribution to journalArticle

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