Colloquium on November, 7 2011

Alfred R. Osborne
Università degli Studi di Torino

Rogue Waves and Holes in  the Sea

I give an overview of a number of historical cases of shipwrecks thought to have been caused by the presence of "rogue waves" in the ocean. Anecdotal evidence of this type has been the principle type of "measurement" made on this phenomenon for the last several thousands of years. Thus the rudimentary understanding of rogue waves has remained primarily in the domain of mariners, and their descriptions of disasters at sea, since the invention of ocean going vessels.

Slowly, over the past 50 years, the continued evolution of the understanding of hydrodynamical phenomena and surface water waves has increased and the requisite mathematical methods and results have continually improved. About 15 years ago it became clear that a number of already discovered results could be applied to the problem of "rogue waves." In particular the most important starting place was the application of known knowledge about the nonlinear Schrödinger equation and the modulational instability: coherent wave packet solutions which "breath", that is they pulsate up and down during their lifetimes.1 Such solutions are not visible by the naked eye for most of their lifetimes, but for short periods they rise up and become "rogue waves," much higher than the background waves. Such solutions are rare in the ocean and even finding them there remains a great challenge today. A considerable amount of work has been conducted in wave tanks around the world, with great success. In these studies it has been found useful to apply particular solutions of the nonlinear Schrödinger equation such as those due to Akhmediev, Peregrine, Ma, Tracy and many others. However, future success will likely depend on advances in several fundamental areas: (1) continued improvements in theoretical developments, (2) continued developments in nonlinear time series analysis methods (we must learn how to analyze nonlinear data), (3) numerical simulations of ocean waves and (4) the understanding of rogue waves in random wave trains in the presence of wind and dissipation. I discuss my involvement in certain recent developments regarding the inverse scattering transform2, applications to ocean engineering and naval architecture3 and extensions to fully three-dimensional waves and hyperfast, hyperaccurate simulations4. I also discuss other directions for future development.

1 These kinds of oceanic rogue waves are hyperbolic analogues of the elliptic vortex solutions of hydrodynamics.

2 Osborne, A. R., Nonlinear Ocean Waves and the Inverse Scattering Transform, Academic Press, 976 pages, 2010.

3 Osborne, A. R., The Sinking of the Prestige: Were Rogue Waves Involved?, Elsevier, 2011.

4 Osborne, A. R., Rogue Waves and Holes in the Sea, Elsevier, 2012.