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Secondary instability and tertiary states in rotating plane Couette flow

Published online by Cambridge University Press:  14 November 2014

C. A. Daly ,
Tobias M. Schneider ,
Philipp Schlatter  and
N. Peake
C. A. Daly*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Tobias M. Schneider
Affiliation:
Max Planck Institute for Dynamics and Self-Organization, Am Fassberg 17, D-37077 Göttingen, Germany ECPS, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
Philipp Schlatter
Affiliation:
Linné FLOW Centre, KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
N. Peake
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: [email protected]
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Abstract

Recent experimental studies have shown rich transition behaviour in rotating plane Couette flow (RPCF). In this paper we study the transition in supercritical RPCF theoretically by determination of equilibrium and periodic orbit tertiary states via Floquet analysis on secondary Taylor vortex solutions. Two new tertiary states are discovered which we name oscillatory wavy vortex flow (oWVF) and skewed vortex flow (SVF). We present the bifurcation routes and stability properties of these new tertiary states and, in addition, we describe a bifurcation procedure whereby a set of defected wavy twist vortices is approached. Further to this, transition scenarios at flow parameters relevant to experimental works are investigated by computation of the set of stable attractors which exist on a large domain. The physically observed flow states are shown to share features with states in our set of attractors.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Instability: Nonlinear instability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 761 , 25 December 2014 , pp. 27 - 61
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Copyright
© 2014 Cambridge University Press 

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