OSCILLATIONS IN A COUPLED BAY-RIVER SYSTEM .2. NUMERICAL-METHOD

Natural and wave-induced oscillations in Nagasaki Bay, a coupled bay-r iver system, are numerically studied. Formulation of the problem is ba sed on the mild slope wave equation with modeled dissipation. Computat ions are performed by the finite element method originated from the cl assical variational principle. The numerical results show that the bay at the mean tidal level has natural modes of periods of 30.60 minutes , 17.28 minutes, 10.08 minutes, 7.67 minutes, etc. The 30.60-minute mo de of the bay is characterized by a monotonic increase of the amplitud e of oscillation from the bay entrance to the Urakami River mouth, whe reas the 17.28-minute mode and the 10.08-minute mode attain maximum ne ar Fukahori. It is also demonstrated that the 30.60-minute mode, the 1 7.28-minute mode and the 10.08-minute mode can be most severely resona ted when the bay is subjected to oscillations in the open sea with per iods of about 33.2 minutes, 17.9 minutes, and 10.1 minutes, respective ly. The existence of the Urakami River seems to have an effect on miti gating the resonant bay oscillations, particularly if the relevant mod e is of relatively low frequency and maximizes near the river mouth.