A multifractal model for the momentum transfer process in wall-bounded flows

X. I.A. Yang, A. Lozano-Durán

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

The cascading process of turbulent kinetic energy from large-scale fluid motions to small-scale and lesser-scale fluid motions in isotropic turbulence may be modelled as a hierarchical random multiplicative process according to the multifractal formalism. In this work, we show that the same formalism might also be used to model the cascading process of momentum in wall-bounded turbulent flows. However, instead of being a multiplicative process, the momentum cascade process is additive. The proposed multifractal model is used for describing the flow kinematics of the low-pass filtered streamwise wall-shear stress fluctuation τl, where l is the filtering length scale. According to the multifractal formalism, (τ'2) ∼ log(Reτ)) and (exp(pτ'l)∼(L/l)ζp in the log-region, where Reτ is the friction Reynolds number, p is a real number, L is an outer length scale and ζp is the anomalous exponent of the momentum cascade. These scalings are supported by the data from a direct numerical simulation of channel flow at Reτ = 4200.

Original languageEnglish (US)
Pages (from-to)R2
JournalJournal of Fluid Mechanics
Volume824
DOIs
StatePublished - Aug 10 2017

Fingerprint

wall flow
Wall flow
Momentum transfer
momentum transfer
Momentum
formalism
momentum
Fluids
Direct numerical simulation
Channel flow
Random processes
cascades
Kinetic energy
Turbulent flow
Shear stress
Kinematics
Reynolds number
Turbulence
real numbers
isotropic turbulence

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

@article{0556aa42d6e84b13bc955d458a618d57,
title = "A multifractal model for the momentum transfer process in wall-bounded flows",
abstract = "The cascading process of turbulent kinetic energy from large-scale fluid motions to small-scale and lesser-scale fluid motions in isotropic turbulence may be modelled as a hierarchical random multiplicative process according to the multifractal formalism. In this work, we show that the same formalism might also be used to model the cascading process of momentum in wall-bounded turbulent flows. However, instead of being a multiplicative process, the momentum cascade process is additive. The proposed multifractal model is used for describing the flow kinematics of the low-pass filtered streamwise wall-shear stress fluctuation τl, where l is the filtering length scale. According to the multifractal formalism, (τ'2) ∼ log(Reτ)) and (exp(pτ'l)∼(L/l)ζp in the log-region, where Reτ is the friction Reynolds number, p is a real number, L is an outer length scale and ζp is the anomalous exponent of the momentum cascade. These scalings are supported by the data from a direct numerical simulation of channel flow at Reτ = 4200.",
author = "Yang, {X. I.A.} and A. Lozano-Dur{\'a}n",
year = "2017",
month = "8",
day = "10",
doi = "10.1017/jfm.2017.406",
language = "English (US)",
volume = "824",
pages = "R2",
journal = "Journal of Fluid Mechanics",
issn = "0022-1120",
publisher = "Cambridge University Press",

}

A multifractal model for the momentum transfer process in wall-bounded flows. / Yang, X. I.A.; Lozano-Durán, A.

In: Journal of Fluid Mechanics, Vol. 824, 10.08.2017, p. R2.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A multifractal model for the momentum transfer process in wall-bounded flows

AU - Yang, X. I.A.

AU - Lozano-Durán, A.

PY - 2017/8/10

Y1 - 2017/8/10

N2 - The cascading process of turbulent kinetic energy from large-scale fluid motions to small-scale and lesser-scale fluid motions in isotropic turbulence may be modelled as a hierarchical random multiplicative process according to the multifractal formalism. In this work, we show that the same formalism might also be used to model the cascading process of momentum in wall-bounded turbulent flows. However, instead of being a multiplicative process, the momentum cascade process is additive. The proposed multifractal model is used for describing the flow kinematics of the low-pass filtered streamwise wall-shear stress fluctuation τl, where l is the filtering length scale. According to the multifractal formalism, (τ'2) ∼ log(Reτ)) and (exp(pτ'l)∼(L/l)ζp in the log-region, where Reτ is the friction Reynolds number, p is a real number, L is an outer length scale and ζp is the anomalous exponent of the momentum cascade. These scalings are supported by the data from a direct numerical simulation of channel flow at Reτ = 4200.

AB - The cascading process of turbulent kinetic energy from large-scale fluid motions to small-scale and lesser-scale fluid motions in isotropic turbulence may be modelled as a hierarchical random multiplicative process according to the multifractal formalism. In this work, we show that the same formalism might also be used to model the cascading process of momentum in wall-bounded turbulent flows. However, instead of being a multiplicative process, the momentum cascade process is additive. The proposed multifractal model is used for describing the flow kinematics of the low-pass filtered streamwise wall-shear stress fluctuation τl, where l is the filtering length scale. According to the multifractal formalism, (τ'2) ∼ log(Reτ)) and (exp(pτ'l)∼(L/l)ζp in the log-region, where Reτ is the friction Reynolds number, p is a real number, L is an outer length scale and ζp is the anomalous exponent of the momentum cascade. These scalings are supported by the data from a direct numerical simulation of channel flow at Reτ = 4200.

UR - http://www.scopus.com/inward/record.url?scp=85022319551&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85022319551&partnerID=8YFLogxK

U2 - 10.1017/jfm.2017.406

DO - 10.1017/jfm.2017.406

M3 - Article

AN - SCOPUS:85022319551

VL - 824

SP - R2

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -