Oscillations in a coupled bay—river system. 2. Numerical method

Abstract

Natural and wave-induced oscillations in Nagasaki Bay, a coupled bay—river system, are numerically studied. Formulation of the problem is based on the mild slope wave equation with modeled dissipation. Computations are performed by the finite element method originated from the classical 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 mode of the bay is characterized by a monotonic increase of the amplitude of oscillation from the bay entrance to the Urakami River mouth, whereas the 17.28-minute mode and the 10.08-minute mode attain maximum near Fukahori. It is also demonstrated that the 30.60-minute mode, the 17.28-minute mode and the 10.08-minute mode can be most severely resonated when the bay is subjected to oscillations in the open sea with periods of about 33.2 minutes, 17.9 minutes, and 10.1 minutes, respectively. The existence of the Urakami River seems to have an effect on mitigating the resonant bay oscillations, particularly if the relevant mode is of relatively low frequency and maximizes near the river mouth.