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Bifurcation and multiple states in plane Couette flow with spanwise rotation

Published online by Cambridge University Press:  03 March 2021

Xiang I. A. Yang Open the ORCID record for Xiang I. A. Yang [Opens in a new window]  and
Zhenhua Xia Open the ORCID record for Zhenhua Xia [Opens in a new window]
Xiang I. A. Yang
Affiliation:
Mechanical and Nuclear Engineering, Pennsylvania State University, State College, PA16802, USA
Zhenhua Xia*
Affiliation:
Department of Engineering Mechanics, Zhejiang University, Hangzhou310027, PR China
*
†Email address for correspondence: xiazh@zju.edu.cn
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Abstract

We present a derivation that begins with the Navier–Stokes equation and ends with a prediction of multiple statistically stable states identical to those observed in a spanwise rotating plane Couette flow. This derivation is able to explain the presence of multiple states in fully developed turbulence and the selection of one state over another by differently sized computational domains and different initial conditions. According to the present derivation, two and only two statistically stable states are possible in an infinitely large plane Couette flow with spanwise rotation, and that multiple states are not possible at very slow or very rapid rotation speeds. We also show the existence of limit-cycle-like behaviours near statistically stable states.

JFM classification

Geophysical and Geological Flows: Rotating flows Turbulent Flows: Rotating turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 913 , 25 April 2021 , A49
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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