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Bi-stability of a pendular disk in laminar and turbulent flows

Published online by Cambridge University Press:  05 July 2013

M. Obligado ,
M. Puy  and
M. Bourgoin
M. Obligado
Affiliation:
Laboratoire des Écoulements Géophysiques et Industriels, CNRS/UJF/G-INP UMR 5519, Université de Grenoble, BP53, 38041, Grenoble, France
M. Puy
Affiliation:
Laboratoire des Écoulements Géophysiques et Industriels, CNRS/UJF/G-INP UMR 5519, Université de Grenoble, BP53, 38041, Grenoble, France
M. Bourgoin*
Affiliation:
Laboratoire des Écoulements Géophysiques et Industriels, CNRS/UJF/G-INP UMR 5519, Université de Grenoble, BP53, 38041, Grenoble, France
*
†Email address for correspondence: mickael.bourgoin@hmg.inpg.fr
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Abstract

The simple pendulum remains one of the most fundamental systems studied in physics. It is commonly used as a model to illustrate a broad variety of mechanisms in a wide range of areas. However, in spite of this popularity, subtle behaviours still remain to be discovered and to be explored when the pendulum is strongly coupled to fluid mechanics. This is for instance illustrated in recent studies by Neill, Livelybrooks & Donnelly (Am. J. Phys., vol. 75, 2007, pp. 226–229) and Bolster, Hershberger & Donnelly (Phys. Rev. E, vol. 81, 2010, pp. 1–6) which highlight the impact on a simple spherical pendulum of vortex shedding and added mass effects. In the present work we show that the equilibrium of a pendular disk facing a flow exhibits bi-stability and hysteresis. We give a simple interpretation of this behaviour in terms of a two-potential-well description, only requiring to know the angular dependence of the normal drag coefficient of an inclined plate. We investigate the influence of turbulence on the equilibrium of the pendulum in general and on the observed bi-stability in particular. Our results have potentially important fundamental and practical consequences: (i) they extend the attractiveness of the pendulum as a model to investigate generic questions related to bi-stable stochastic processes, (ii) they highlight important fluid dynamic mechanisms, including turbulent drag enhancement and fluid–structure interaction issues.

JFM classification

Aerodynamics: Aerodynamics Aerodynamics: Flow-structure interactions Turbulent Flows: Turbulent Flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 728 , 10 August 2013 , R2
Copyright
©2013 Cambridge University Press 

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