Nonlinear Fourier Classification of 663 Rogue Waves Measured in the Philippine Sea

Abstract

Rogue waves are spontaneous extreme waves whose wave heights are at least twice the significant wave height of the surrounding waves. The formation of rogue waves has been attributed to several possible mechanisms such as linear superposition of random waves, dispersive focusing, and modulational instability. Breather solutions of the nonlinear Schrödinger equation (NLSE) are furthermore often considered prototypical rogue waves. The dominant generation mechanisms of rogue waves in the real ocean are currently not well understood because actual field measurements are scarce. In this study, exploiting twelve years of field measurement data from an ocean buoy, we apply the nonlinear Fourier transform (NFT) for the NLSE (NLSE-NFT) to a large dataset of measured rogue waves. While the NLSE-NFT has been used to analyze rogue waves before, this is the first time that it is systematically applied to a large real-world dataset. Since different types of nonlinear waves have distinctive nonlinear spectral portraits, we categorize the measured rogue waves into four types based on the characteristics of the largest nonlinear mode: stable, small breather, large breather and soliton. If NLSE breather solutions really are prototypical rogue waves, one would expect the breather types to be the most common. The classification results for the rogue-wave samples are discussed and, furthermore, compared with those for a similar amount of non-rogue wave samples. Finally, the question whether the largest nonlinear mode can be attributed to a rogue wave is investigated for a part of the data set.