Asymptotic Solutions of Resonances in Harbors with Connected Basins

Asymptotic formulas for the resonant wave numbers are obtained for harbors with connected basins. The number of basins is taken to be two in this paper. However, generalization of the formulas for harbors with more than two basins can easily be obtained. The harbor and the ocean are assumed to have a constant depth. The coast is assumed to be straight but the boundaries of the basins can assume arbitrary shapes. In deriving the asymptotic formulas, the widths of the entrances to each basin are assumed to be small compared with the incident wave length and also with the dimensions of the basins. Comparisons with existing numerical results, however, indicate that these formulas are good even when the entrance widths are comparable to the incident wave lengths and to the dimensions of the basins. The formulas depend only on the eigenvalues of the closed basins and the corresponding normal mode solutions as at entrances. Furthermore, each resonant wave number depends only on the normal modes with wave numbers close to it.