OSCILLATIONS IN A COUPLED BAY-RIVER SYSTEM .1. ANALYTIC SOLUTION

Wave induced oscillations in a coupled bay-river system are analyzed. Efforts are devoted to clarifying the geometric effects of the river w ith different physical features. The formulation includes modeled diss ipation 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 inte rest. The analytic results show that a semi-infinite river is simply t o provide an exit for the resonant wave energy to be radiated so that the bay oscillations are mitigated. No appreciable change of the reson ant wave numbers owing to the existence of the semi-infinite river has been observed. If coupled with an enclosed channel, the bay may be ag itated 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 i s 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 whi ch the resonant wave energy may be radiated, the ''harbor paradox'' se ems to be no longer an appropriate statement.