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Stability of acoustic propagation in 2D duct flows: A low frequency approach

Anne-Sophie Bonnet-Ben Dhia 1 Marc Duruflé 2 Patrick Joly 1 Lauris Joubert 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
2 IMB - Institut de Mathématiques de Bordeaux
Abstract : In this paper, we derive a simplified "quasi-1D" limit model for the propagation of low frequency acoustic waves in a laminar flow filling a 2D duct. We analyze the well-posedness of this model in function of the Mach profile of the flow. This can be reduced to the study of the spectrum of a bounded non-normal operator. As a by-product of this analysis, we establish new results for hydrodynamic instabilities of KelvinHelmholtz type in compressible fluids. © 2011 World Scientific Publishing Company.
Keywords : Spectral theory hydrodynamic stability acoustics in flow asymptotic analysis
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https://hal-ensta-paris.archives-ouvertes.fr//hal-00849576
Contributor : Aurélien Arnoux <>
Submitted on : Friday, August 30, 2013 - 3:20:02 PM
Last modification on : Monday, January 13, 2020 - 2:38:06 PM

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Anne-Sophie Bonnet-Ben Dhia, Marc Duruflé, Patrick Joly, Lauris Joubert. Stability of acoustic propagation in 2D duct flows: A low frequency approach. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2011, 21 (5), pp.1121-1151. ⟨10.1142/s0218202511005271⟩. ⟨hal-00849576⟩

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