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Multiple states in turbulent plane Couette flow with spanwise rotation

Published online by Cambridge University Press:  28 December 2017

Zhenhua Xia*
Affiliation:
Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China
Yipeng Shi
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, China
Qingdong Cai
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, China
Minping Wan
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, China
Shiyi Chen*
Affiliation:
Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, China State Key Laboratory for Turbulence and Complex Systems, Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, China Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, China
*
Email addresses for correspondence: xiazh@zju.edu.cn, chensy@sustc.edu.cn
Email addresses for correspondence: xiazh@zju.edu.cn, chensy@sustc.edu.cn

Abstract

Turbulence is ubiquitous in nature and engineering applications. Although Kolmogorov’s (C. R. Acad. Sci. URSS, vol. 30, 1941a, pp. 301–305; Dokl. Akad. Nauk URSS, vol. 30, 1941b, pp. 538–540) theory suggested a unique turbulent state for high Reynolds numbers, multiple states were reported for several flow problems, such as Rayleigh–Bénard convection and Taylor–Couette flows. In this paper, we report that multiple states also exist for turbulent plane Couette flow with spanwise rotation through direct numerical simulations at rotation number $Ro=0.2$ and Reynolds number $Re_{w}=1300$ based on the angular velocity in the spanwise direction and half of the wall velocity difference. With two different initial flow fields, our results show that the flow statistics, including the mean streamwise velocity and Reynolds stresses, show different profiles. These different flow statistics are closely related to the flow structures in the domain, where one state corresponds to two pairs of roll cells, and the other shows three pairs. The present result enriches the studies on multiple states in turbulence.

Type
JFM Papers
Copyright
© 2017 Cambridge University Press 

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Xia et al. supplementary movie 1

Snapshots of instantaneous velocity vectors in cross-section at x=0 from Case R2_512

Download Xia et al. supplementary movie 1(Video)
Video 5.7 MB

Xia et al. supplementary movie 2

Snapshots of instantaneous velocity vectors in cross-section at x=0 from Case R3_512

Download Xia et al. supplementary movie 2(Video)
Video 5.1 MB