Numerical Study of Transient Harbor Oscillations Induced by N-Waves

The response amplitudes of different resonant modes in an elongated harbor with constant depth induced by N-waves with different amplitudes and different types are calculated using the Normal Mode Decomposition (NMD) method. Wave conditions inside the harbor are simulated with a fully nonlinear Boussinesq model FUNWAVE-TVD. It is found that, for the small amplitude of the incident N-wave, wave energy inside the harbor is dominated by the lowest few modes, while only a small proportion of the wave energy is distributed over the higher modes. However, with the increase of the incident wave amplitude, most of the wave energy inside the harbor tends to concentrate on the higher resonant modes, hence the relative wave energy distributed over the lowest few modes decreases. On the other hand, the wave energy distribution inside the harbor is also significantly affected by the type of the N-wave. The wave energy inside the harbor excited by the MS-type incident N-wave is more concentrated than that excited by the TS-type N-wave. The MS- and TS-type N-waves correspond to the N-wave expressions proposed by Madsen and Schäffer (Madsen, Schäffer, 2010. Analytical solutions for tsunami runup on a plane beach single waves, N-waves and transient waves. Journal of Fluid Mechanics 645, 27–57) and Tadepalli and Synolakis (Tadepalli, Synolakis, 1994. The run-up of N-waves on sloping beaches. Proceedings of the Royal Society London A: Mathematical, Physical & Engineering Sciences 445, 99–112), respectively.