Focussed wave groups on deep and shallow water

The evolution of steep uni-directional wave groups with realistic spectra is studied using an efficient and robust numerical scheme due to Craig and Sulem. The size of the wave group at the instant of focus, defined as the occurrence of the highest (or lowest) surface elevation at any time, is strongly affected by the water depth. In deep water (Kd to approximately 4), the highest waves are considerably higher and the groups more compact than predicted by linear or 2^nd order wave theory. As the depth is reduced to Kd to approximately 1, the predominately 3^rd order wave-wave interactions responsible for the non-linear evolution of the group are much weaker - in contrast to the mostly 2^nd order vertical asymmetry of the wave group, which is much stronger in shallower water. The wave kinematics for these groups is also discussed. For these isolated groups particularly on shallow water, the return flow associated with the localized set-down beneath the group is very large.