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The Heated Bénard–Kármán Street: A Review of the Effective Reynolds Number Concept

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Nonlinear Waves and Pattern Dynamics

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Abstract

This chapter focuses on the wake flow behind a heated circular cylinder in the laminar vortex shedding regime where the Bénard–Kármán street appears. This flow is of fundamental importance both from the viewpoint of the hydrodynamic stability theory and engineering applications. Even in absence of buoyancy forces, this wake flow is more complicated than in the isothermal case due to temperature differences generated within the fluid leading to variations of its physical properties. In this situation, experiments showed that heat is never a passive contaminant. Due to the respective thermal dependence of the kinematic viscosity, heating the cylinder stabilizes the flow in air while it destabilizes the flow in water. This phenomenon led to the definition of an effective Reynolds number that is associated to an effective temperature. Value of the effective temperature is shown to depend on the nature of the fluid. In air, global and local flow similarities between wake flows of the same “effective” Reynolds numbers are pointed out, underlying the physical significance of this concept.

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Acknowledgements

The authors would like to thank past collaborators on the subject of this chapter including Laurence Hamma, Stéphane LeMasson, Fabien Dumouchel, Franck Weiss and Gilles Godard. The authors gratefully acknowledge the assistance of the technical staff of CNRS UMR 6614. During these researches, owing to the support of CNRS, we have also had the privilege to work with Alexander Ezersky. We remember Alexander as a brilliant scientist both renowned theorist, skilled experimenter and a great man.

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  1. Laboratoire de Thermodynamique CNRS UMR 6614 – CORIA, Université de Rouen Site Universitaire du Madrillet, 675, Avenue de L’Université, BP 12, 76801 Cedex, Saint Etienne du Rouvray, France

    Pierre Paranthoën & Jean-Claude Lecordier

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  1. Pierre Paranthoën
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  2. Jean-Claude Lecordier
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Correspondence to Pierre Paranthoën .

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  1. Normandie Université, UNICAEN, UNIROUEN, CNRS, UMR 6143, M2C, Caen, France

    Nizar Abcha

  2. Department of Nonlinear Geophysical Processes, Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia

    Efim Pelinovsky

  3. Normandie Université, Unihavre, CNRS, UMR 6294, LOMC, Le Havre CX, France

    Innocent Mutabazi

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Paranthoën, P., Lecordier, JC. (2018). The Heated Bénard–Kármán Street: A Review of the Effective Reynolds Number Concept. In: Abcha, N., Pelinovsky, E., Mutabazi, I. (eds) Nonlinear Waves and Pattern Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-319-78193-8_12

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