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Phase trapping and slipping in a forced hydrodynamically self-excited jet

Published online by Cambridge University Press:  29 October 2013

Larry K. B. Li  and
Matthew P. Juniper
Larry K. B. Li*
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
Matthew P. Juniper
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
*
†Email address for correspondence: l.li@gatescambridge.org
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Abstract

In a recent study on a coupled laser system, Thévenin et al. (Phys. Rev. Lett., vol. 107, 2011, 104101) reported the first experimental evidence of phase trapping, a partially synchronous state characterized by frequency locking without phase locking. To determine whether this state can arise in a hydrodynamic system, we reanalyse the data from our recent experiment on a periodically forced self-excited low-density jet (J. Fluid Mech., vol. 726, 2013, pp. 624–655). We find that this jet exhibits the full range of phase dynamics predicted by model oscillators with weak nonlinearity. These dynamics include (i) phase trapping between phase drifting and phase locking when the jet is forced far from its natural frequency and (ii) phase slipping during phase drifting when it is forced close to its natural frequency. This raises the possibility that similar phase dynamics can be found in other similarly self-excited flows. It also strengthens the validity of using low-dimensional nonlinear dynamical systems based on a universal amplitude equation to model such flows, many of which are of industrial importance.

JFM classification

Instability: Absolute/convective instability Flow Control: Flow Control Nonlinear Dynamical Systems: Nonlinear Dynamical Systems
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 735 , 25 November 2013 , R5
Copyright
©2013 Cambridge University Press 

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