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Reynolds number effects on a velocity–vorticity correlation-based skin-friction drag decomposition in incompressible turbulent channel flows

Published online by Cambridge University Press:  11 January 2024

Yunchao Zhao ,
Yitong Fan Open the ORCID record for Yitong Fan [Opens in a new window]  and
Weipeng Li Open the ORCID record for Weipeng Li [Opens in a new window]
Yunchao Zhao
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, PR China
Yitong Fan
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, PR China Department of Mechanical Engineering, University of Melbourne, Parkville, VIC 3010, Australia
Weipeng Li*
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, PR China
*
†Email address for correspondence: liweipeng@sjtu.edu.cn
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Abstract

A form of skin-friction drag decomposition is given based on the velocity–vorticity correlations, $\langle v\omega _z\rangle$ and $\langle -w\omega _y\rangle$, which represent the advective vorticity transport and vortex stretching, respectively. This identity provides a perspective to understand the mechanism of skin-friction drag generation from vortical motions and it has better physical interpretability compared with some previous studies. The skin-friction coefficients in incompressible turbulent channel flows at friction Reynolds numbers from 186 to 2003 are divided with this velocity–vorticity correlation-based identity. We mainly focus on the Reynolds number effects on the contributing terms, their scale-dependence and quadrant characteristics. Results show that the contributing terms and their proportions exhibit similarities and the same peak locations across the wall layer. For the first time, we find that the positive and negative regions in the spanwise pre-multiplied spectra of the turbulent inertia ($\langle v'\omega _z'\rangle +\langle -w'\omega _y'\rangle$) can be separated with a universal linear relationship of $\lambda _z^+=3.75y^+$. The linear relationship is adopted as the criterion to investigate the scale dependence of the velocity–vorticity coupling structures. It reveals that the negative and positive structures dominate the generation of friction drag associated with the advective vorticity transport and vortex stretching, respectively. Moreover, quadrant analyses of the velocity–vorticity correlations are performed to further examine the friction drag generation related to different quadrant motions.

JFM classification

Waves/Free-surface Flows: Channel flow Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 979 , 25 January 2024 , A20
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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