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Intermittent dynamics in simple models of the turbulent wall layer

Published online by Cambridge University Press:  26 April 2006

Gal Berkooz ,
Philip Holmes  and
J. L. Lumley
Gal Berkooz
Affiliation:
Center for Applied Mathematics, Ithaca, NY 14853-7501, USA
Philip Holmes
Affiliation:
Departments of Theoretical and Applied Mechanics and Mathematics, Ithaca, NY 14853-7501, USA
J. L. Lumley
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Ithaca, NY 14853-7501, USA
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Abstract

We generalize the class of models of the wall layer of Aubry et al. (1988), based on the proper orthogonal decomposition, to permit uncoupled evolution of streamwise and cross-stream disturbances. Since the Reynolds stress is no longer constrained, in the absence of streamwise spatial variations all perturbation velocity components eventually decay to zero. However, their transient behaviour is dominated by ’ghosts’ of the non-trivial fixed points and attracting heteroclinic cycles which are characteristic features of those models based on empirical eigenfunctions whose individual velocity components are fixed. This suggests that the intermittent events observed in Aubry et al. do not arise solely because of the effective closure assumption incorporated in those models, but are rooted deeper in the dynamical phenomenon of the wall region.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 230 , September 1991 , pp. 75 - 95
Copyright
© 1991 Cambridge University Press

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