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Experimental study of a Neimark–Sacker bifurcation in axially forced Taylor–Couette flow

Published online by Cambridge University Press:  04 July 2006

MANISH SINHA ,
IOANNIS G. KEVREKIDIS  and
ALEXANDER J. SMITS
MANISH SINHA
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University Princeton, NJ 08544-0710, USA
IOANNIS G. KEVREKIDIS
Affiliation:
Department of Chemical Engineering, PACM and Mathematics, Princeton University, Princeton, NJ 08544-0710, USA
ALEXANDER J. SMITS
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University Princeton, NJ 08544-0710, USA
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Abstract

A variation of the classical Taylor–Couette system is studied where, with the outer cylinder stationary, the inner cylinder rotates at constant angular velocity while executing harmonic oscillations in the axial direction. Experiments reveal a Hopf (Neimark–Sacker) bifurcation from a limit cycle to a torus. Alternating bands of frequency-locked and quasi-periodic flow are observed and identified. Power spectral plots and (delay reconstructed) Poincaré maps are used to characterize the temporal dynamics. Results are presented on the rotation number variation across parameter space, the shape and growth of frequency-locked resonance horns, and the spatial development of the flow considerably beyond the primary transition surface.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 558 , 10 July 2006 , pp. 1 - 32
Copyright
© 2006 Cambridge University Press

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