2015/01/14 by Francesco Fedele, Fedele, Francesco · 3 citations
Earth and Planetary Sciences · #Atmospheric and Oceanic Physics (physics.ao-ph) #Coastal and Marine Dynamics #FOS: Physical sciences #Ocean Waves and Remote Sensing #Tropical and Extratropical Cyclones Research
paper · pdf · doi:10.48550/arxiv.1501.03370
openalex publication_date 2015/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a new conceptual framework for the prediction of rogue waves and third-order space-time extremes of wind seas that relies on the Tayfun (1980) and Janssen (2009) models coupled with Adler-Taylor (2009) theory on the Euler characteristics of random fields. Extreme statistics of the Andrea rogue wave event are examined capitalizing on European Reanalysis (ERA)-interim data. A refinement of Janssen's (2003) theory suggests that in realistic oceanic seas characterized by short-crested multidirectional waves, homogeneous and Gaussian initial conditions become irrelevant as the wave field adjusts to a non-Gaussian state dominated by bound nonlinearities over time scales t≫ tc≈0.13T0/νσθ, where T0, ν and σθ denote mean wave period, spectral bandwidth and angular spreading of dominant waves. For the Andrea storm, ERA-interim predictions yield tc/T0∼ O(1) indicating that quasi-resonant interactions are negligible. Further, the mean maximum sea surface height expected over the Ekofisk platform's area is higher than that expected at a fixed point. However, both of these statistics underestimate the actual crest height hobs∼1.63Hs observed at a point near the Ekofisk site, where Hs is the significant wave height. To explain the nature of such extreme, we account for both skewness and kurtosis effects and consider the threshold hq exceeded with probability q by the maximum surface height of a sea state over an area in time. We find that hobs nearly coincides with the threshold h1/1000∼1.62Hs estimated at a point for a typical 3-hour sea state, suggesting that the Andrea rogue wave is likely to be a rare occurrence in quasi-Gaussian seas.
simple-idealized-1d-nlse: Pseudo-Spectral Solver for the 1D Nonlinear Schrödinger Equation