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Secondary instability and tertiary states in rotating plane Couette flow. (English) Zbl 1308.76294
Summary: 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.

MSC:
76U05 General theory of rotating fluids
76E30 Nonlinear effects in hydrodynamic stability
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
76F06 Transition to turbulence
76F20 Dynamical systems approach to turbulence
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