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Flow structures in spanwise rotating plane Poiseuille flow based on thermal analogy

Published online by Cambridge University Press:  23 December 2021

Shengqi Zhang ,
Zhenhua Xia Open the ORCID record for Zhenhua Xia [Opens in a new window]  and
Shiyi Chen
Shengqi Zhang
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing 100871, PR China
Zhenhua Xia*
Affiliation:
Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, PR China
Shiyi Chen
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Peking University, Beijing 100871, PR China Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China
*
†Email address for correspondence: xiazh@zju.edu.cn
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Abstract

The analogy between rotating shear flow and thermal convection suggests the existence of plumes, inertial waves and plume currents in plane Poiseuille flow under spanwise rotation. The existence of these flow structures is examined with the results of three-dimensional and two-dimensional three-component direct numerical simulations. The dynamics of plumes near the unstable side is embodied in a truncated exponential distribution of turbulent fluctuations. For large rotation numbers, inertial waves are identified near the stable side, and these can be used to explain the abnormal flow statistics, such as the large root-mean-square of the streamwise velocity fluctuation and the nearly negligible Reynolds shear stress. For small or medium rotation numbers, plumes generated from the unstable side form large-scale plume currents and the patterns of the plume currents show different capabilities in scalar transport.

JFM classification

Convection: Buoyancy-driven instability Turbulent Flows: Rotating turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 933 , 25 February 2022 , A24
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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Zhang et al. supplementary movie 1

Contour of $u'$ in the $y-z$ plane from the 2-D case at $Re_\tau=180, Ro_\tau=5$. The dashed and dash-dotted lines denote the horizontal locations at $y=y_1$ and $y=y_2$ with $N_b(y_1)=0.1N_b(-1)$ and $N_b(y_2)=0.1N_b(1)$ respectively.

Download Zhang et al. supplementary movie 1(Video)
Video 8 MB

Zhang et al. supplementary movie 2

Contour of $u'$ in the $y-z$ plane from the 2-D case at $Re_\tau=180, Ro_\tau=40$. The dashed and dash-dotted lines denote the horizontal locations at $y=y_1$ and $y=y_2$ with $N_b(y_1)=0.1N_b(-1)$ and $N_b(y_2)=0.1N_b(1)$ respectively.

Download Zhang et al. supplementary movie 2(Video)
Video 8.1 MB

Zhang et al. supplementary movie 3

Contour of $u'$ in the $y-z$ plane at $x=0$ from the 3-D case at $Re_\tau=180, Ro_\tau=5$. The dashed and dash-dotted lines denote the horizontal locations at $y=y_1$ and $y=y_2$ with $N_b(y_1)=0.1N_b(-1)$ and $N_b(y_2)=0.1N_b(1)$ respectively.

Download Zhang et al. supplementary movie 3(Video)
Video 8.2 MB

Zhang et al. supplementary movie 4

Contour of $u'$ in the $y-z$ plane at $x=0$ from the 3-D case at $Re_\tau=180, Ro_\tau=40$. The dashed and dash-dotted lines denote the horizontal locations at $y=y_1$ and $y=y_2$ with $N_b(y_1)=0.1N_b(-1)$ and $N_b(y_2)=0.1N_b(1)$ respectively.

Download Zhang et al. supplementary movie 4(Video)
Video 8.4 MB
Supplementary material: PDF

Zhang et al. supplementary material

Captions for movies 1-4

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