Journal of Applied Mathematics
Volume 2007 (2007), Article ID 80205, 17 pages
doi:10.1155/2007/80205
Research Article

Waves Trapped by Submerged Obstacles at High Frequencies

A. M. Marín,1 R. D. Ortíz,1 and P. Zhevandrov2,3

1Instituto de Matemáticas Aplicadas, Universidad de Cartagena, Sede Piedra de Bolívar, Cartagena de Indias, Bolívar, Colombia
2Facultad de Ciencias Físico-Matemáticas, Universidad Michoacana, Edificio B, Ciudad Universitaria, 58060 Morelia, Michoacán, Mexico
3Facultad de Ingeniería, Universidad de la Sabana, Campus Puente del Común, Km. 21 Autopista Norte, Chía, Cundinamarca, Colombia

Received 10 November 2006; Accepted 25 June 2007

Academic Editor: Matiur Rahman

Copyright © 2007 A. M. Marín et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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).