2014/02/18 by A. Hadjihosseini, Ali Hadjihosseini, J. Peinke +3
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Classical mechanics #Closure (psychology) #Fokker–Planck equation #Fractional Differential Equations Solutions #Law #Markov chain #Markov process #Mathematics #Nonlinear system #Ocean Waves and Remote Sensing #Oceanographic and Atmospheric Processes #Partial differential equation #Physics #Quantum mechanics #Rogue wave #Scale (ratio) #Statistical physics #Statistics #Stochastic process #Wave equation #physics.ao-ph #physics.data-an
paper · pdf · doi:10.1088/1367-2630/16/5/053037
18 pages, 13 figures
arxiv created 2014/02/18 · openalex publication_date 2014/05/21 · arxiv updated 2015/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.