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Minnaert resonances for acoustic waves in bubbly media

by H. Ammari and B. Fitzpatrick and D. Gontier and H. Lee and H. Zhang

(Report number 2016-18)

Abstract
Through the application of layer potential techniques and Gohberg-Sigal theory we derive an original formula for the Minnaert resonance frequencies of arbitrarily shaped bubbles. We also provide a mathematical justification for the monopole approximation of scattering of acoustic waves by bubbles at their Minnaert resonant frequency. Our results are complemented by several numerical examples which serve to validate our formula in two dimensions.

Keywords: Minnaert resonance, bubble, monopole approximation, layer potentials, acoustic waves.

@Techreport{AFGLZ16_655,
  author = {H. Ammari and B. Fitzpatrick and D. Gontier and H. Lee and H. Zhang},
  title = {Minnaert resonances for acoustic waves in bubbly media},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2016-18},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2016/2016-18.pdf },
  year = {2016}
}

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