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Transition to chaos through period doublings of a forced oscillating cylinder in steady current

Published online by Cambridge University Press:  21 January 2020

Liang Cheng ,
Xiaoying Ju Open the ORCID record for Xiaoying Ju [Opens in a new window] ,
Feifei Tong Open the ORCID record for Feifei Tong [Opens in a new window]  and
Hongwei An Open the ORCID record for Hongwei An [Opens in a new window]
Liang Cheng
Affiliation:
School of Engineering, The University of Western Australia, 35 Stirling Highway, Perth, WA 6009, Australia DUT-UWA Joint Research Centre, State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, No. 2 Linggong Road, Dalian116024, China
Xiaoying Ju*
Affiliation:
School of Engineering, The University of Western Australia, 35 Stirling Highway, Perth, WA 6009, Australia
Feifei Tong
Affiliation:
School of Engineering, The University of Western Australia, 35 Stirling Highway, Perth, WA 6009, Australia
Hongwei An
Affiliation:
School of Engineering, The University of Western Australia, 35 Stirling Highway, Perth, WA 6009, Australia
*
†Email address for correspondence: [email protected]
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Abstract

Transition to chaos through a cascade of period doublings of the primary $1/2$ synchronization mode is discovered in steady approaching flow around a forced inline oscillating cylinder near a plane boundary at a Reynolds number $(Re)$ of 175. The transition occurs well within the otherwise synchronized region (known as the Arnold tongue) in the frequency and amplitude space of the oscillating cylinder, creating two parameter strips of desynchronized flows within the Arnold tongue. Five orders of period doublings from mode $1/2$ to mode $16/32$ are revealed by progressively increasing the frequency resolution in the simulation. The ratio of frequency intervals of two successive period-doubling modes asymptotes towards the first Feigenbaum constant, reaching a value of 4.52 at mode of $16/32$. Additional three-dimensional simulations demonstrate the existence of period doubling with a regular spanwise flow structure similar to regular mode B of steady flow around an isolated cylinder. Although transition to chaos through cascades of period doublings is primarily reported for the primary $1/2$ synchronization mode, it is also observed for other synchronization modes $(p/q)$ (Tang et al., J. Fluid Mech., vol. 832, 2017, pp. 146–169), where $p$ and $q$ are integers with a non-reducible $p/q$, such as $2/3$. The physical mechanisms responsible for the present period-doubling bifurcations and transition to chaos through cascades of period doublings are ascribed to the interaction of asymmetric vortex shedding from the cylinder (due to a geometric asymmetry) and the boundary layer developed on the plane boundary, through specifically designed numerical tests.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Vortex Flows: Vortex dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 887 , 25 March 2020 , A5
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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