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Quasi-periodic intermittency in oscillating cylinder flow

Published online by Cambridge University Press:  12 September 2017

Bryan Glaz Open the ORCID record for Bryan Glaz [Opens in a new window] ,
Igor Mezić ,
Maria Fonoberova  and
Sophie Loire
Bryan Glaz*
Affiliation:
Vehicle Technology Directorate, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005, USA
Igor Mezić
Affiliation:
Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, CA 93106, USA
Maria Fonoberova
Affiliation:
Aimdyn, Inc., Santa Barbara, CA 93106, USA
Sophie Loire
Affiliation:
Aimdyn, Inc., Santa Barbara, CA 93106, USA
*
†Email address for correspondence: bryan.j.glaz.civ@mail.mil
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Abstract

Fluid dynamics induced by periodically forced flow around a cylinder is analysed computationally for the case when the forcing frequency is much lower than the von Kármán vortex shedding frequency corresponding to the constant flow velocity condition. By using the Koopman mode decomposition approach, we find a new normal form equation that extends the classical Hopf bifurcation normal form by a time-dependent term for Reynolds numbers close to the Hopf bifurcation value. The normal form describes the dynamics of an observable and features a forcing (control) term that multiplies the state, and is thus a parametric – i.e. not an additive – forcing effect. We find that the dynamics of the flow in this regime is characterized by alternating instances of quiescent and strong oscillatory behaviour and that this pattern persists indefinitely. Furthermore, the spectrum of the associated Koopman operator is shown to possess quasi-periodic features. We establish the theoretical underpinnings of this phenomenon – that we name quasi-periodic intermittency – using the new normal form model and show that the dynamics is caused by the tendency of the flow to oscillate between the unstable fixed point and the stable limit cycle of the unforced flow. The quasi-periodic intermittency phenomenon is also characterized by positive finite-time Lyapunov exponents that, over a long period of time, asymptotically approach zero.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Nonlinear Dynamical Systems: Low-dimensional models Vortex Flows: Vortex Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 828 , 10 October 2017 , pp. 680 - 707
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Copyright
© Cambridge University Press 2017. This is a work of the U.S. Government and is not subject to copyright protection in the United States. 

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