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Algebraically decaying modes and wave packet pseudo-modes in swept Hiemenz flow

Published online by Cambridge University Press:  23 December 2009

DOMINIK OBRIST  and
PETER J. SCHMID
DOMINIK OBRIST*
Affiliation:
Institute of Fluid Dynamics, ETH Zurich, 8092 Zürich, Switzerland
PETER J. SCHMID
Affiliation:
Laboratoire d'Hydrodynamique (LadHyX), CNRS-École Polytechnique, 91128 Palaiseau, France
*
†Email address for correspondence: [email protected]
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Abstract

The modal structure of the swept Hiemenz flow, a model for the flow near the attachment line of a swept wing, consists of eigenfunctions which exhibit (super-)exponential or algebraic decay as the wall-normal coordinate tends to infinity. The subset of algebraically decaying modes corresponds to parts of the spectrum which are characterized by a significant sensitivity to numerical discretization. Numerical evidence further suggests that a continuous spectrum covering a two-dimensional range of the complex plane exists. We investigate the family of uniform swept Hiemenz modes using eigenvalue computations, numerical simulations and the concept of wave packet pseudo-modes. Three distinct branches of the family of algebraically decaying eigenmodes are identified. They can be superimposed to produce wavefronts propagating towards or away from the boundary layer and standing or travelling wave packets in the free stream. Their role in the exchange of information between the free stream and the attachment-line boundary layer for the swept Hiemenz flow is discussed. The concept of wave packet pseudo-modes has been critical in the analysis of this problem and is expected to lead to further insights into other shear flows in semi- or bi-infinite domains.

JFM classification

Instability: Instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 643 , 25 January 2010 , pp. 309 - 332
Copyright
Copyright © Cambridge University Press 2009

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