The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


Paper Information

Paper Title:

Trapping of Water Waves By Underwater Ridges


1A. M. Marin, 1R. D. Ortiz and 2J. A. Rodriguez-Ceballos.

1Facultad de Ciencias Exactas y Naturales
Universidad de Cartagena
Sede Piedra de Bolivar, Avenida del Consulado
Cartagena de Indias, Bolivar,

2Instituto Tecnológico de Morelia Facultad de Ciencias Fisico Matematicas
Universidad Michoacana Tecnológico
1500, Col. Lomas de Santiaguito Edificio Be ,
Ciudad Universitaria, 58120 Morelia, Michoacan,



As is well-known, underwater ridges and submerged horizontal cylinders can serve as waveguides for surface water waves. For large values of the wavenumber in the direction of the ridge, there is only one trapped wave (this was proved in Bonnet & Joly (1993, SIAM J. Appl. Math. 53, pp 1507-1550)).
We construct the asymptotics of these trapped waves and their frequencies at high frequency by means of reducing the initial problem to a pair of boundary integral equations and then by applying the method of Zhevandrov & Merzon (2003, AMS Transl. (2) 208, pp 235-284), in order to solve them.

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