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Three-dimensional transverse instabilities in detached boundary layers

Published online by Cambridge University Press:  04 January 2007

FRANÇOIS GALLAIRE ,
MATTHIEU MARQUILLIE  and
UWE EHRENSTEIN
FRANÇOIS GALLAIRE
Affiliation:
Laboratoire J. A. Dieudonné, Université de Nice-Sophia Antipolis, Parc Valrose, F-06108 Nice Cedex 02, France
MATTHIEU MARQUILLIE
Affiliation:
Laboratoire de Mécanique de Lille, Université des Sciences et Technologies de Lille, Boulevard Paul Langevin, F-59655 Villeneuve d'Ascq Cédex, France
UWE EHRENSTEIN
Affiliation:
Laboratoire J. A. Dieudonné, Université de Nice-Sophia Antipolis, Parc Valrose, F-06108 Nice Cedex 02, France
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Abstract

A direct numerical simulation of the incompressible Navier–Stokes equations of the flow over a bump shows a stationary longitudinal instability at a Reynolds number of Re = 400. A three-dimensional global mode linear analysis is used to interpret these results and shows that the most unstable eigenmode is steady and localized in the recirculation bubble, with spanwise wavelength of approximately ten bump heights. An inviscid geometrical optics analysis along closed streamlines is then proposed and modified to account for viscous effects. This motivates a final discussion regarding the physical origin of the observed instability.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 571 , 25 January 2007 , pp. 221 - 233
Copyright
Copyright © Cambridge University Press 2007

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