Extended self-similarity in moment-generating-functions in wall-bounded turbulence at high Reynolds number

X. I.A. Yang, C. Meneveau, I. Marusic, L. Biferale

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

In wall-bounded turbulence, the moment generating functions (MGFs) of the streamwise velocity fluctuations exp(quz+) develop power-law scaling as a function of the wall normal distance z/δ. Here u is the streamwise velocity fluctuation, + indicates normalization in wall units (averaged friction velocity), z is the distance from the wall, q is an independent variable, and δ is the boundary layer thickness. Previous work has shown that this power-law scaling exists in the log-region 3Reτ0.5z+,z0.15δ where Reτ is the friction velocity-based Reynolds number. Here we present empirical evidence that this self-similar scaling can be extended, including bulk and viscosity-affected regions 30<z+,z<δ, provided the data are interpreted with the Extended-Self-Similarity (ESS), i.e., self-scaling of the MGFs as a function of one reference value, qo. ESS also improves the scaling properties, leading to more precise measurements of the scaling exponents. The analysis is based on hot-wire measurements from boundary layers at Reτ ranging from 2700 to 13000 from the Melbourne High-Reynolds-Number-Turbulent-Boundary-Layer-Wind-Tunnel. Furthermore, we investigate the scalings of the filtered, large-scale velocity fluctuations uzL and of the remaining small-scale component, uzS=uz-uzL. The scaling of uzL falls within the conventionally defined log region and depends on a scale that is proportional to l+∼Reτ1/2; the scaling of uzS extends over a much wider range from z+≈30 to z≈0.5δ. Last, we present a theoretical construction of two multiplicative processes for uzL and uzS that reproduce the empirical findings concerning the scalings properties as functions of z+ and in the ESS sense.

Original languageEnglish (US)
Article number044405
JournalPhysical Review Fluids
Volume1
Issue number4
DOIs
StatePublished - Aug 9 2016

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Moment generating function
Self-similarity
Reynolds number
Turbulence
Scaling
Boundary layers
Scaling laws
Friction
Fluctuations
Boundary Layer
Power Law
Wind tunnels
Wire
Turbulent Boundary Layer
Viscosity
Wind Tunnel
Scaling Exponent
Normalization
Multiplicative
Directly proportional

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Modeling and Simulation
  • Fluid Flow and Transfer Processes

Cite this

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abstract = "In wall-bounded turbulence, the moment generating functions (MGFs) of the streamwise velocity fluctuations exp(quz+) develop power-law scaling as a function of the wall normal distance z/δ. Here u is the streamwise velocity fluctuation, + indicates normalization in wall units (averaged friction velocity), z is the distance from the wall, q is an independent variable, and δ is the boundary layer thickness. Previous work has shown that this power-law scaling exists in the log-region 3Reτ0.5z+,z0.15δ where Reτ is the friction velocity-based Reynolds number. Here we present empirical evidence that this self-similar scaling can be extended, including bulk and viscosity-affected regions 30",
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Extended self-similarity in moment-generating-functions in wall-bounded turbulence at high Reynolds number. / Yang, X. I.A.; Meneveau, C.; Marusic, I.; Biferale, L.

In: Physical Review Fluids, Vol. 1, No. 4, 044405, 09.08.2016.

Research output: Contribution to journalArticle

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