Non-linear scattering of steep surface waves around vertical columns

The free-surface wave elevation within a radius distance around fixed vertical columns is investigated. In particular, the validity of second-order modelling of the wave-column interaction in steep waves is addressed. Numerical models are compared to experimental data for two cases studies, including a single column and a three-column gravity-based structure (GBS). Regular waves are considered. Systematic trends in observed deviations between the theory and experiments are investigated. The analysis covers the first- and second-harmonic amplitudes as well as the total crest amplification. It is found that linear modelling significantly under-predicts the crest amplification, while the second-order correction represents a significant improvement and works generally well in waves with moderate steepness. In waves with high steepness, the models can give roughly useful estimates, at least for longer waves, but there are also discrepancies: first- (basic) harmonic amplitudes are under-predicted, while second-harmonics are generally over-predicted. Physical interpretations are proposed and discussed. It is observed that the increase in the measured basic harmonic relative to linear theory is correlated with the kinetic energy of the incident wave. One possible explanation may be flow separation, but higher-order difference-frequency effects may also contribute. For the second-harmonics, the decrease in the measurements relative to theory shows a correlation with a locally very high steepness of second-harmonic diffracted waves, and could therefore be linked to local dissipation and breaking.