Estimates of the trapped-mode frequencies of oscillation of a liquid in the presence of submerged bodies

The problem of the steady oscillations of an unbounded liquid with a free surface in the presence of a system of submerged horizontal cylindrical bodies of arbitrary cross-section is considered. The problem describes the interaction of bodies with waves which propagate at an arbitrary angle to the generatrix of the system of bodies and, also, the oscillations of a liquid in a channel with vertical walls. The criterion of uniqueness, proposed earlier in [1], is developed to find estimates of the trapped-mode frequencies. Estimates are obtained of the frequencies which are both in the continuous spectrum of the problem as well as outside it. Results of calculations are presented and a comparison is made with existing estimates.