Experimental and numerical study on focused wave generation using different energy modes

This paper reports an experimental and numerical study on the generation of freak waves related to the spatiotemporal focusing mechanism, where multiple water waves converge at a specific point in space and time to produce a large transient wave. A new energy distribution mode of constant-difference wave number (CDK) within the wave group is proposed and applied to both a physical and a numerical flume to generate focused waves, with primary attention given to the water surface elevation, underlying kinematics, and internal spectrum structure during the focused wave generation process. The classical experiment by Baldock et al. [“A laboratory study of nonlinear surface waves on water,” Philos. Trans. R. Soc., Ser. A 354, 649–676 (1996)], which used a constant-difference wave period within the wave group, is chosen for comparison. Spectral analysis shows that the CDK energy distribution mode can easily stimulate multiwave resonance in the focused wave group, where significant energy transfer from the main frequencies to higher harmonics is observed. Compared with the data from Baldock et al. [“A laboratory study of nonlinear surface waves on water,” Philos. Trans. R. Soc., Ser. A 354, 649–676 (1996)], the CDK wave group produces larger focused wave crests with higher propagation speeds and larger velocity gradients near the water surface due to strong multiwave resonance. The effects of the input spectrum, incident amplitude and initial water depth under different energy modes on focused-wave generation are analyzed. All the results indicate that the CDK energy distribution mode can produce larger focused waves compared to other energy distribution modes, which offers a novel approach for generating freak waves in the laboratory.