A LABORATORY STUDY OF NONLINEAR SURFACE-WAVES ON WATER

This paper describes an experimental. investigation in which a large n umber of water waves were focused at one point in space and time to pr oduce a large transient wave group. Measurements of the water surface elevation and the underlying kinematics are compared with both a linea r wave theory and a second-order solution based on the sum of the wave -wave interactions identified by Longuet-Higgins & Stewart (1960). The data shows that the focusing of wave components produces a highly non linear wave group in which the nonlinearity increases with the wave am plitude and reduces with increasing bandwidth. When compared with the first- and second-order solutions, the wave-wave interactions produce a steeper wave envelope in which the central wave crest is higher and narrower, while the adjacent wave troughs are broader and less deep. T he water particle kinematics are also strongly nonlinear. The accumula ted experimental data suggest that the formation of a focused wave gro up involves a significant transfer of energy into both the higher and lower harmonics. This is consistent with an increase in the local ener gy density, and the development of large velocity gradients near the w ater surface. Furthermore, the nonlinear wave-wave interactions are sh own to be fully reversible. However, when compared to a linear solutio n there is a permanent change in the relative phase of the free waves. This explains the downstream shifting of the focus point (Longuet-Hig gins 1974), and appears to be similar to the phase changes which resul t from the nonlinear interaction of solitons travelling at different v elocities (Yuen & Lake 1982).