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Onset of vortex structures in rotating plane Couette flow

Published online by Cambridge University Press:  05 May 2021

Masato Nagata Open the ORCID record for Masato Nagata [Opens in a new window] ,
Baofang Song Open the ORCID record for Baofang Song [Opens in a new window]  and
Darren P. Wall
Masato Nagata*
Affiliation:
School of Mechanical Engineering, Tianjin University, Tianjin300072, People's Republic of China Graduate School of Engineering, Kyoto University, Kyoto615-8530, Japan
Baofang Song
Affiliation:
Center for Applied Mathematics, Tianjin University, Tianjin300072, People's Republic of China
Darren P. Wall
Affiliation:
Faculty of Engineering, Kyushu University, Fukuoka819-0395, Japan
*
†Email address for correspondence: nagata.masato.45x@st.kyoto-u.ac.jp
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Abstract

Two new flows, a tilted-vortex flow and a periodic-vortex flow, are found numerically at the onset of instability in rotating plane Couette flow (RPCF). It has hitherto been believed that the first few bifurcation sequences from the laminar state are quite well understood, namely, that a streamwise-independent flow with a two-dimensional roll-cell (2dRC) structure bifurcates first, followed by the bifurcation of a wavy-vortex flow (WVF). The present study shows that the 2dRC is, in fact, unstable from its onset, and that the newly found tilted-vortex flow takes over in place of 2dRC. It is further found that the periodic-vortex flow takes part in the early stages of laminar–turbulent transition. The existence of the new flows can be verified by careful examinations of the experimental observations in Hiwatashi et al. (Phys. Fluids, vol. 19, 2007, 048103) and Kawata & Alfredsson (J. Fluid Mech., vol. 791, 2016, 191–213).

JFM classification

Nonlinear Dynamical Systems: Bifurcation Instability: Shear-flow instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 918 , 10 July 2021 , A2
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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