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Fano resonances in acoustics

Published online by Cambridge University Press:  26 October 2010

STEFAN HEIN ,
WERNER KOCH  and
LOTHAR NANNEN
STEFAN HEIN
Affiliation:
Institut für Aerodynamik und Strömungstechnik, DLR Göttingen, 37073 Göttingen, Germany
WERNER KOCH*
Affiliation:
Institut für Aerodynamik und Strömungstechnik, DLR Göttingen, 37073 Göttingen, Germany
LOTHAR NANNEN
Affiliation:
Institut für Numerische und Angewandte Mathematik, Universität Göttingen, 37083 Göttingen, Germany
*
†Email address for correspondence: werner.koch@dlr.de
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Abstract

In contrast to completely open systems, laterally confined domains can sustain localized, truly trapped modes with nominally zero radiation loss. These discrete resonant modes cannot be excited linearly by the continuous propagating duct modes due to symmetry constraints. If the symmetry of the geometry is broken the trapped modes become highly localized quasi-trapped modes which can interfere with the propagating duct modes. The resulting narrowband Fano resonances with resonance and antiresonance features are a generic phenomenon in all scattering problems with multiple resonant pathways. This paper deals with the classical scattering of acoustic waves by various obstacles such as hard-walled single and multiple circular cylinders or rectangular and wedge-like screens in a two-dimensional duct without mean flow. The transmission and reflection coefficients as well as the (complex) resonances are computed numerically by means of the finite-element method in conjunction with two different absorbing boundary conditions, namely the complex scaling method and the Hardy space method. The results exhibit the typical asymmetric Fano line shapes near the trapped-mode resonances if the symmetry of the geometry is broken.

JFM classification

Acoustics: Acoustics Acoustics: Noise control Waves/Free-surface Flows: Wave scattering
Type
Papers
Information
Journal of Fluid Mechanics , Volume 664 , 10 December 2010 , pp. 238 - 264
Copyright
Copyright © Cambridge University Press 2010

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References

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