## Abstract

The dominant paradigm in turbulent wall flows is that the mean velocity near the wall, when scaled on wall variables, is independent of the friction Reynolds number Re_{τ}. This paradigm faces challenges when applied to fluctuations but has received serious attention only recently. Here, we present a promising perspective, and support it with data, that fluctuations displaying non-zero wall-values, or near-wall peaks, are bounded for large values of Re_{τ}, owing to the natural constraint that the dissipation rate is bounded. Specifically, Φ_{∞}-Φ =C_{Φ}Re_{τ}^{-1/4}, where Φ represents the maximum value of any of the following quantities: energy dissipation rate, turbulent diffusion, fluctuations of pressure, streamwise and spanwise velocities, squares of vorticity components, and the wall values of pressure and shear stresses; the subscript ∞ denotes the bounded asymptotic value of Φ and the coefficient C_{Φ} depends on Φ but not on Re_{τ}. Moreover, there exists a scaling law for the maximum value in the wall-normal direction of high-order moments, of the form 〈ϕ^{2q}〉^{1/q}_{max} = α_{q}-β_{q}Re_{τ}^{-1/4}, where ϕ represents the streamwise or spanwise velocity fluctuation and α_{q} and β_{q} are independent on Re_{τ}. Excellent agreement with available data is observed. A stochastic process for which the random variable has the form just mentioned, referred to here as the 'linear q-norm Gaussian', is proposed to explain the observed linear dependence of α_{q} on q.

Original language | English (US) |
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State | Published - 2022 |

Event | 12th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2022 - Osaka, Virtual, Japan Duration: Jul 19 2022 → Jul 22 2022 |

### Conference

Conference | 12th International Symposium on Turbulence and Shear Flow Phenomena, TSFP 2022 |
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Country/Territory | Japan |

City | Osaka, Virtual |

Period | 7/19/22 → 7/22/22 |

## ASJC Scopus subject areas

- Aerospace Engineering
- Atmospheric Science