Oscillations in a coupled bay-river system. 1. Analytic solution

Abstract Wave induced oscillations in a coupled bay-river system are analyzed. Efforts are devoted to clarifying the geometric effects of the river with different physical features. The formulation includes modeled dissipation in both the bay and the river. The solution method is patching formal expressions derived for the complex amplitude of water surface oscillation in geometrically regular subregions of the domain of interest. The analytic results show that a semi-infinite river is simply to provide an exit for the resonant wave energy to be radiated so that the bay oscillations are mitigated. No appreciable change of the resonant wave numbers owing to the existence of the semi-infinite river has been observed. If coupled with an enclosed channel, the bay may be agitated at not only the natural modes of the bay but also those of the river. The “harbor paradox” is qualitatively valid even as the bay is dissipative. However, if a semi-infinite river is in presence, that is, if there is at least a part of the boundary of the bay through which the resonant wave energy may be radiated, the “harbor paradox” seems to be no longer an appropriate statement.