High-frequency asymptotics of waves trapped by underwater ridges and submerged cylinders

  • Authors:

  • A. M. Marí/n;R. D. Ortí/z;P. Zhevandrov

  • Affiliations:

  • Institute of Physics and Mathematics, University of Michoacan, Morelia, Mexico on leave from University of Cartagena, Cartagena, Colombia;Institute of Physics and Mathematics, University of Michoacan, Morelia, Mexico on leave from University of Cartagena, Cartagena, Colombia;Universidad de la Sabana, Chia, Colombia/ on sabbatical leave from Faculty of Physics and Mathematics, University of Michoacan, Morelia, Mexico

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2007

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Abstract

As is well-known, underwater ridges and submerged horizontal cylinders can serve as waveguides for surface water waves. For large values of the wavenumber k in the direction the ridge, there is only one trapped wave (this was proved in Bonnet-Ben Dhia and Joly [Mathematical analysis of guided water waves, SIAM J. Appl. Math. 53 (1993) 1507-1550]. We construct asymptotics of these trapped waves and their frequencies as k-~ by means of reducing the initial problem to a pair of boundary integral equations and then by applying the method of Zhevandrov and Merzon [Asymptotics of eigenfunctions in shallow potential wells and related problems, Amer. Math. Soc. Trans. 208 (2) (2003) 235-284], in order to solve them.