### 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 language | English (US) |
---|---|

Article number | 044405 |

Journal | Physical Review Fluids |

Volume | 1 |

Issue number | 4 |

DOIs | |

State | Published - Aug 9 2016 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Physical Review Fluids*,

*1*(4), [044405]. https://doi.org/10.1103/PhysRevFluids.1.044405

}

*Physical Review Fluids*, vol. 1, no. 4, 044405. https://doi.org/10.1103/PhysRevFluids.1.044405

**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.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Extended self-similarity in moment-generating-functions in wall-bounded turbulence at high Reynolds number

AU - Yang, X. I.A.

AU - Meneveau, C.

AU - Marusic, I.

AU - Biferale, L.

PY - 2016/8/9

Y1 - 2016/8/9

N2 - 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

AB - 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

UR - http://www.scopus.com/inward/record.url?scp=85021171948&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85021171948&partnerID=8YFLogxK

U2 - 10.1103/PhysRevFluids.1.044405

DO - 10.1103/PhysRevFluids.1.044405

M3 - Article

AN - SCOPUS:85021171948

VL - 1

JO - Physical Review Fluids

JF - Physical Review Fluids

SN - 2469-990X

IS - 4

M1 - 044405

ER -