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Algebraically diverging modes upstream of a swept bluff body

Published online by Cambridge University Press:  02 August 2011

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: obrist@ifd.mavt.ethz.ch
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Abstract

Classical stability theory for swept leading-edge boundary layers predicts eigenmodes in the free stream with algebraic decay far from the leading edge. In this article, we extend the classical base flow solution by Hiemenz to a uniformly valid solution for the flow upstream of a bluff body, which includes a three-dimensional boundary layer, an inviscid stagnation-point flow and an outer parallel flow. This extended, uniformly valid base flow additionally supports modes which diverge algebraically outside the boundary layer. The theory of wave packet pseudomodes is employed to derive analytical results for the growth rates and for the eigenvalue spectra of this type of mode. The complete spectral analysis of the flow, including the algebraically diverging modes, will give a more appropriate basis for receptivity studies and will more accurately describe the interaction of perturbations in the free stream with disturbances in the boundary layer.

JFM classification

Boundary Layers: Boundary layer receptivity Boundary Layers: Boundary layer stability Instability: Instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 683 , 25 September 2011 , pp. 346 - 356
Copyright
Copyright © Cambridge University Press 2011

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