Journal of Fluid Mechanics

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Supercritical transition to turbulence in an inertially driven von Kármán closed flow

FLORENT RAVELETa1 p1, ARNAUD CHIFFAUDELa1 and FRANÇOIS DAVIAUDa1

a1 Service de Physique de l'Etat Condensé, Direction des Sciences de la Matière, CEA-Saclay, CNRS URA 2464, 91191 Gif-sur-Yvette cedex, France

Abstract

We study the transition from laminar flow to fully developed turbulence for an inertially driven von Kármán flow between two counter-rotating large impellers fitted with curved blades over a wide range of Reynolds number (102–106). The transition is driven by the destabilization of the azimuthal shear layer, i.e. Kelvin–Helmholtz instability, which exhibits travelling/drifting waves, modulated travelling waves and chaos before the emergence of a turbulent spectrum. A local quantity – the energy of the velocity fluctuations at a given point – and a global quantity – the applied torque – are used to monitor the dynamics. The local quantity defines a critical Reynolds number Rec for the onset of time-dependence in the flow, and an upper threshold/crossover Ret for the saturation of the energy cascade. The dimensionless drag coefficient, i.e. the turbulent dissipation, reaches a plateau above this finite Ret, as expected for ‘Kolmogorov’-like turbulence for Re→∞. Our observations suggest that the transition to turbulence in this closed flow is globally supercritical: the energy of the velocity fluctuations can be considered as an order parameter characterizing the dynamics from the first laminar time-dependence to the fully developed turbulence. Spectral analysis in the temporal domain, moreover, reveals that almost all of the fluctuation energy is stored in time scales one or two orders of magnitude slower than the time scale based on impeller frequency.

(Received December 05 2006)

(Revised January 18 2008)

Correspondence:

p1 Present address: Laboratory for Aero and Hydrodynamics, Leeghwaterstraat 21, 2628 CA Delft, The Netherlands.

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