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Secondary instability and tertiary states in rotating plane Couette flow

  • C. A. Daly (a1), Tobias M. Schneider (a2) (a3), Philipp Schlatter (a4) and N. Peake (a1)

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.

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Email address for correspondence: cdaly87@gmail.com

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Secondary instability and tertiary states in rotating plane Couette flow

  • C. A. Daly (a1), Tobias M. Schneider (a2) (a3), Philipp Schlatter (a4) and N. Peake (a1)

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