Waves Trapped by Submerged Obstacles at High Frequencies

Abstract

As is well known, submerged horizontal cylinders can serve as wavegorderes 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 $k\to \infty$ 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).