Quantification of Extreme Events in Nonlinear Ocean Waves

Extreme ocean or rogue waves is one of the most important open topics for ocean engineering both because of their catastrophic impact on ships and coastal structures but also because of the serious lack of specialized mathematical tools for the analysis of the underlying physics. An informal definition of an extreme water wave would describe it as a wave with height twice as large as the significant wave height. Through the large number of hits and/or observations of extreme waves as well as the results of numerical simulations it has now been well established that extreme waves occur much more frequently than it was initially believed and that their traditional characterization as ‘rare events’ severely underestimates the frequency of their occurrence.

Extreme waves are associated with non-Gaussian statistics and strongly nonlinear dynamics as their intermittent character and strong spatial localization properties manifests. Existing quantification methods of random events cannot handle such requirements since they are usually relying on low order statistics. The goal of the proposed work is the development of the necessary theoretical and computational tools that would allow for the efficient quantification and analysis of extreme events in the oceanic environment carefully taking into account all the requirements and restrictions of the problem, such us consideration of the nonlinear mechanisms and the non-Gaussian statistics.

To achieve this goal, it is necessary first to develop a statistical analysis methodology and tools focused on the specific requirements of problems associated with rare events. Subsequently, we plan to develop blended stochastic techniques that would allow for the effective evolution of the statistics by handling different dynamical components differently depending on their complexity. Finally the above machinery will be applied to specific water wave models in order to analyze their statistical responses and correlate those to nonlinear dynamical properties.