Experimental investigation of the Peregrine Breather of gravity waves on finite water depth

A series of laboratory experiments were performed to study the Peregrine Breather (PB) evolution in a wave flume of finite depth and deep water. Experimental cases were selected with water depths k(0)h (k(0 )is the wave number and h is the water depth) varying from 3.11 to 8.17 and initial steepness k(0)a(0) (a(0) is the background wave amplitude) in the range 0.06 to 0.12, and the corresponding initial Ursell number in the range 0.03 to 0.061. Experimental results indicate that the water depth plays an important role in the formation of the extreme waves in finite depth; the maximum wave amplification of the PB packets is also strongly dependent on the initial Ursell number. For experimental cases with the initial Ursell number larger than 0.05, the maximum crest amplification can exceed three. If the initial Ursell number is nearly 0.05, a shorter propagation distance is needed for maximum amplification of the height in deeper water. A time-frequency analysis using the wavelet transform reveals that the energy of the higher harmonics is almost in-phase with the carrier wave. The contribution of the higher harmonics to the extreme wave is significant for the cases with initial Ursell number larger than 0.05 in water depth k(0)h < 5.0. Additionally, the experimental results are compared with computations based on both the nonlinear Schrodinger (NLS) equation and the Dysthe equation, both with a dissipation term. It is found that both models with a dissipation term can predict the maximum amplitude amplification of the primary waves. However, the Dysthe equation also can predict the group horizontal asymmetry.