Trapped modes of oscillation of a liquid for surface-piercing bodies in oblique waves

The linear problem of the harmonic oscillations of an ideal incompressible heavy liquid with a free surface in the presence of two and more infinitely long partially submerged cylindrical bodies of arbitrary cross-section is considered. It is proved that there are configurations of the bodies which provide examples of the non-uniqueness of the boundary-value problem in the case of an arbitrary frequency of the oscillations and an arbitrary non-ze ro angle between the generatrix of the cylinders and the direction of propa gation of the surface waves. In the case of these configurations, the homog eneous boundary-value problem has nontrivial solutions with a finite energy integral, which describe trapped modes of oscillation of the liquid. (C) 1 999 Elsevier Science Ltd. All rights reserved.