Prof. D. Faulkner emphasized the importance of the study of extreme/rogue waves when he noted that the use of sine waves for computing pressures in the design of ships was no longer tenable, primarily because of the large number of cases where extreme structural damage has been encountered due to highly nonlinear large waves. This perspective resulted in the creation of the European program MaxWave and the subsequent program Extreme Seas soon followed. Recently my own studies of nonlinear effects in water waves at Nonlinear Waves Research Corporation (NWRC) have resulted in a number of successes with regard to the fundamental physical understanding of rogue waves. These studies enlarge our ability to understand the requisite impact of extreme waves on the design of ships. Some of these advances are:
(1) The determination of analytical techniques for describing rogue wave packets in two dimensions for random sea states which are directionally spread.
(2) The description of wave overturning and breaking in directional sea states with the Type II (lateral) instability.
(3) The development of hyperfast computer models for the deterministic simulation of directional sea states.
(4) The development of a fast approach for computing the full Boltzmann integral (FBI) for the nonlinear wave/wave interactions in wind/wave models.
(5) The identification of the actual physical location in the power spectrum for the nonlinear Fourier rogue wave components.
(6) The development of nonlinear Fourier techniques for analyzing times series of ocean waves for the presence of rogue wave states.
(7) The development of fully nonlinear directional spectra (in terms of frequency and direction) from arrays of instruments.
(8) The development of hindcasting and predicting capability for the assessment of the onset of a rogue sea.
I also discuss a number of future developments now underway at NWRC.