### 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 τ_{l}, where l is the filtering length scale. According to the multifractal formalism, (τ'^{2}) ∼ log(Re_{τ})) and (exp(pτ'_{l})∼(L/l)ζ_{p} in the log-region, where Re_{τ} is the friction Reynolds number, p is a real number, L is an outer length scale and ζ_{p} is the anomalous exponent of the momentum cascade. These scalings are supported by the data from a direct numerical simulation of channel flow at Re_{τ} = 4200.

Original language | English (US) |
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Pages (from-to) | R2 |

Journal | Journal of Fluid Mechanics |

Volume | 824 |

DOIs | |

State | Published - Aug 10 2017 |

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### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering

### Cite this

*Journal of Fluid Mechanics*,

*824*, R2. https://doi.org/10.1017/jfm.2017.406

}

*Journal of Fluid Mechanics*, vol. 824, pp. R2. https://doi.org/10.1017/jfm.2017.406

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

Research output: Contribution to journal › Article

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

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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 -