Numerical study of low-frequency waves during harbor resonance

• Boussinesq model is used to simulate the harbor resonance induced by wave groups.
• A method is proposed to decompose low-frequency components during harbor resonance.
• The amplitude ratio of bound to free long waves is closely related to short waves.

The aim of this paper is to investigate how bound and free long waves and their relative components change with respect to short wavelengths when resonance occurs in a long and narrow rectangular harbor. Long-period oscillations excited by bichromatic primary waves are simulated using the Boussinesq model. A separation procedure is proposed to decompose the low-frequency components inside the harbor into bound and free long waves. For comparison, the non-resonant wave condition is also considered. It shows that the amplitudes of bound and free long waves and their ratio are closely related to the short wavelengths, regardless of whether the harbor is resonant or not. For the given harbor and primary wave frequency ranges studied in this paper, when the harbor is at the lowest resonant mode, the amplitudes of bound long waves are always lower than those of free long waves but tend to be larger than half of the latter when the average short wavelengths are larger than 0.66 times the harbor length. When the harbor is non-resonant and the average short wavelengths are larger than 0.56 times the harbor length, the former is inclined to be larger than the latter.