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National Technical University of Athens, Greece

The author should be congratulated for a very interesting theoretical-numerical paper with various practical applications. The paper describes a fully nonlinear 3-D simulation method for the assessment of strong nonlinear effects in wavebody interaction problems. As an example of application and validation of the developed computer code, the results of Fig.15 hold for an incident wave period equal to twice the natural heaving period of the studied floating body. For this particular case, the amplitude of the 2ω motion component appears to be quite significant, namely about 20% of the fundamental frequency component. Could the author explain how these results change, when the wave excitation period is equal to the simple natural heaving period of the floating cylinder? Do the higher-order motion components become relatively larger?


Thank you for your kind comment. I ran the numerical model in the conditions you were interested in, i.e., for an incident wave period equal to the natural heaving frequency of the floating cylinder. The resulting vertical motion of the body is plotted in Figure A1. Contrary to the simulation presented in the paper, the present signal is almost purely monochromatic, with an amplification factor equal to about 1.7 with respect to the incident wave amplitude. Higher harmonics are negligible, but there is sensible negative vertical drift, as shown by Figure A2 representing the moving window Fourier analysis of the time series. The wave amplitude is A/H=0.025, the wave period is T*sqrt(g/H)=3.5, and the wave length is λ/H=1.956.

In this resonant regime, body and free surface tend to move with opposite phases, and runs with larger wave amplitudes led to numerical breakdown, the bottom of the body getting very close to aerating. This problem could be solved by implementing a more refined remeshing procedure for the body, instead of the simple redistribution of nodes in the vertical direction used for the present simulations.

Fig. A1: Vertical motion of the body. A/H=0.025; T*sqrt(g/H)=3.5

Fig. A2: Harmonic components of the motion

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