Journal of Applied Mathematics (Jan 2007)

Waves Trapped by Submerged Obstacles at High Frequencies

  • A. M. Marín,
  • R. D. Ortíz,
  • P. Zhevandrov

DOI
https://doi.org/10.1155/2007/80205
Journal volume & issue
Vol. 2007

Abstract

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As is well known, submerged horizontal cylinders can serve as waveguides for surface water waves. For large values of the wavenumber k in the direction of the cylinders, there is only one trapped wave. We construct asymptotics of these trapped modes and their frequencies as k→∞ in the case of one or two submerged cylinders by means of reducing the initial problem to a system of integral equations on the boundaries and then solving them using a technique suggested by Zhevandrov and Merzon (2003).