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Transition to turbulence through steep global-modes cascade in an open rotating cavity

Published online by Cambridge University Press:  28 October 2011

Bertrand Viaud ,
Eric Serre  and
Jean-Marc Chomaz
Bertrand Viaud*
Affiliation:
Centre de Recherche de l’Armée de l’Air, CReA BA701 13661 Salon de Provence, France M2P2, CNRS Universités Aix Marseille, IMT Chateau-Gombert 13451 Marseille, France
Eric Serre
Affiliation:
M2P2, CNRS Universités Aix Marseille, IMT Chateau-Gombert 13451 Marseille, France
Jean-Marc Chomaz
Affiliation:
LadHyX, CNRS-Ecole Polytechnique, F-91128 Palaiseau, France
*
†Email address for correspondence: bertrand.viaud@supaero.org
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Abstract

The transition to turbulence in a rotating boundary layer is analysed via direct numerical simulation (DNS) in an annular cavity made of two parallel corotating discs of finite radial extent, with a forced inflow at the hub and free outflow at the rim. In a former numerical investigation (Viaud, Serre & Chomaz J. Fluid Mech., vol. 598, 2008, pp. 451–464) realized in a sectorial cavity of azimuthal extent , we have established the existence of a primary bifurcation to nonlinear global mode with angular phase velocity and radial envelope coherent with the so-called elephant mode theory. The former study has demonstrated the subcritical nature of this primary bifurcation with a base flow that keeps being linearly stable for all Reynolds numbers studied. The present work investigates the stability of this elephant mode by extending the cavity both in the radial and azimuthal direction. When the Reynolds number based on the forced throughflow is increased above a threshold value for the existence of the nonlinear global mode, a large-amplitude impulsive perturbation gives rise to a self-sustained saturated wave with characteristics identical to the 68-fold global elephant mode obtained in the smaller cavity. This saturated wave is itself globally unstable and a second front appears in the lee of the primary where small-scale instability develops. These secondary instabilities are identical for the and the long sectorial cavities, indicating that transition involves a Floquet mode of zero azimuthal wavenumber. This secondary instability leads to a very disorganized state, defining the transition to turbulence. The observed transition to turbulence linked to the secondary instability of a global mode confirms, for the first time on a real flow, the possibility of a direct transition to turbulence through an elephant mode cascade, a scenario that was up to now only observed on the Ginzburg–Landau model.

JFM classification

Instability: Absolute/convective instability Boundary Layers: Boundary layer stability Geophysical and Geological Flows: Rotating flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 688 , 10 December 2011 , pp. 493 - 506
Copyright
Copyright © Cambridge University Press 2011

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