Minnaert resonances for acoustic waves in bubbly media

  • Habib Ammari

    Department of Mathematics, ETH Zürich, Rämistrasse 101, CH-8092 Zürich, Switzerland
  • Brian Fitzpatrick

    Department of Mathematics, ETH Zürich, Rämistrasse 101, CH-8092 Zürich, Switzerland
  • David Gontier

    Department of Mathematics, ETH Zürich, Rämistrasse 101, CH-8092 Zürich, Switzerland
  • Hyundae Lee

    Department of Mathematics, Inha University, 253 Yonghyun-dong Nam-gu, Incheon 402-751, Republic of Korea
  • Hai Zhang

    Department of Mathematics, HKUST, Clear Water Bay, Kowloon, Hong Kong
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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.

Cite this article

Habib Ammari, Brian Fitzpatrick, David Gontier, Hyundae Lee, Hai Zhang, Minnaert resonances for acoustic waves in bubbly media. Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 7, pp. 1975–1998

DOI 10.1016/J.ANIHPC.2018.03.007