Stochastic analysis of ocean wave states with and without rogue waves

Abstract

This work presents an analysis of ocean wave data including rogue waves. A stochastic approach based on the theory of Markov processes is applied. With this analysis we achieve a characterization of the scale-dependent complexity of ocean waves by means of a Fokker-Planck equation, providing stochastic information on multi-scale processes. In particular, we show evidence of Markov properties for increment processes, which means that a three-point closure for the complexity of the wave structures seems to be valid. Furthermore, we estimate the parameters of the Fokker-Planck equation by parameter-free data analysis. The resulting Fokker-Planck equations are verified by numerical reconstruction. This work presents a new approach where the coherent structure of rogue waves seems to be integrated into the fundamental statistics of complex wave states. © 2014 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.