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Modal and non-modal linear stability of the plane Bingham–Poiseuille flow

Published online by Cambridge University Press:  19 April 2007

C. NOUAR ,
N. KABOUYA ,
J. DUSEK  and
M. MAMOU
C. NOUAR
Affiliation:
LEMTA, UMR 7563 (CNRS-INPL-UHP), 2 Avenue de la Fort de Haye, BP 160 54504 Vandoeuvre Lès Nancy, Francecherif.nouar@ensem.inpl-nancy.fr
N. KABOUYA
Affiliation:
LEMTA, UMR 7563 (CNRS-INPL-UHP), 2 Avenue de la Fort de Haye, BP 160 54504 Vandoeuvre Lès Nancy, Francecherif.nouar@ensem.inpl-nancy.fr
J. DUSEK
Affiliation:
IMFS Strasbourg, UMR 7507 (CNRS-ULP) 2 Rue Boussingault, 67000 Strasbourg, France
M. MAMOU
Affiliation:
Institute for Aerospace Research (IAR) National Research Council (NRC), Montreal Road, Ottawa, Ontario, Canada, K1A 0R6
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Abstract

The receptivity problem of plane Bingham–Poiseuille flow with respect to weak perturbations is addressed. The relevance of this study is highlighted by the linear stability analysis results (spectra and pseudospectra). The first part of the present paper thus deals with the classical normal-mode approach in which the resulting eigenvalue problem is solved using the Chebychev collocation method. Within the range of parameters considered, the Poiseuille flow of Bingham fluid is found to be linearly stable. The second part investigates the most amplified perturbations using the non-modal approach. At a very low Bingham number (B ≪ 1), the optimal disturbance consists of almost streamwise vortices, whereas at moderate or large B the optimal disturbance becomes oblique. The evolution of the obliqueness as function of B is determined. The linear analysis presented also indicates, as a first stage of a theoretical investigation, the principal challenges of a more complete nonlinear study.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 577 , 25 April 2007 , pp. 211 - 239
Copyright
Copyright © Cambridge University Press 2007

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