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Robust relation of streamwise velocity autocorrelation in atmospheric surface layers based on an autoregressive moving average model

Published online by Cambridge University Press:  21 February 2024

Fei-Chi Zhang Open the ORCID record for Fei-Chi Zhang [Opens in a new window] ,
Jin-Han Xie Open the ORCID record for Jin-Han Xie [Opens in a new window] ,
Song Xi Chen Open the ORCID record for Song Xi Chen [Opens in a new window]  and
Xiaojing Zheng Open the ORCID record for Xiaojing Zheng [Opens in a new window]
Fei-Chi Zhang
Affiliation:
Department of Mechanics and Engineering Science at College of Engineering, and State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing 100871, PR China
Jin-Han Xie*
Affiliation:
Department of Mechanics and Engineering Science at College of Engineering, and State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing 100871, PR China Joint Laboratory of Marine Hydrodynamics and Ocean Engineering, Laoshan Laboratory, Shandong 266237, PR China
Song Xi Chen*
Affiliation:
School of Mathematical Sciences, Guanghua School of Management and Center for Statistical Science, Peking University, Beijing 100871, PR China
Xiaojing Zheng*
Affiliation:
Department of Mechanics and Engineering Science at College of Engineering, and State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing 100871, PR China Center for Particle-Laden Turbulence, Lanzhou University, Lanzhou 730000, PR China
*
†Email addresses for correspondence: jinhanxie@pku.edu.cn, csx@gsm.pku.edu.cn, xjzheng@lzu.edu.cn
†Email addresses for correspondence: jinhanxie@pku.edu.cn, csx@gsm.pku.edu.cn, xjzheng@lzu.edu.cn
†Email addresses for correspondence: jinhanxie@pku.edu.cn, csx@gsm.pku.edu.cn, xjzheng@lzu.edu.cn
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Abstract

We construct an autoregressive moving average (ARMA) model consisting of the history and random effects for the streamwise velocity fluctuation in boundary-layer turbulence. The distance to the wall and the boundary-layer thickness determine the time step and the order of the ARMA model, respectively. Based on the autocorrelation's analytical expression of the ARMA model, we obtain a global analytical expression for the second-order structure function, which asymptotically captures the inertial, dynamic and large-scale ranges. Specifically, the exponential autocorrelation of the ARMA model arises from the autoregressive coefficients and is modified to logarithmic behaviour by the moving-average coefficients. The asymptotic expressions enable us to determine model coefficients by existing parameters, such as the Kolmogorov and the Townsend–Perry constants. A consequent double-log expression for the characteristic length scale is derived and is justified by direct numerical simulation data with $Re_\tau \approx 5200$ and field-measured neutral atmospheric surface layer data with $Re_\tau \sim O(10^6)$ from the Qingtu Lake Observation Array site. This relation is robust because it applies to $Re_\tau$ from $O(10^4)$ to $O(10^6)$, and even when the statistics of natural ASL deviate from those of canonical boundary-layer turbulence, e.g. in the case of imbalance in energy production and dissipation, and when the Townsend–Perry constant deviates from traditional values.

JFM classification

Geophysical and Geological Flows: Atmospheric flows Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 981 , 25 February 2024 , A20
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© The Author(s), 2024. Published by Cambridge University Press

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