Real world ocean rogue waves explained without the modulational instability (original) (raw)

Since the 1990s, the modulational instability has commonly been used to explain the occurrence of rogue waves that appear from nowhere in the open ocean. However, the importance of this instability in the context of ocean waves is not well established. This mechanism has been successfully studied in laboratory experiments and in mathematical studies, but there is no consensus on what actually takes place in the ocean. In this work, we question the oceanic relevance of this paradigm. In particular, we analyze several sets of field data in various European locations with various tools, and find that the main generation mechanism for rogue waves is the constructive interference of elementary waves enhanced by second-order bound nonlinearities and not the modulational instability. This implies that rogue waves are likely to be rare occurrences of weakly nonlinear random seas. According to the most commonly used definition, rogue waves are unusually large-amplitude waves that appear from nowhere in the open ocean. Evidence that such extremes can occur in nature is provided, among others, by the Draupner and Andrea events, which have been extensively studied over the last decade 1–6. Several physical mechanisms have been proposed to explain the occurrence of such waves 7 , including the two competing hypotheses of nonlinear focusing due to third-order quasi-resonant wave-wave interactions 8 , and purely disper-sive focusing of second-order non-resonant or bound harmonic waves, which do not satisfy the linear dispersion relation 9,10. In particular, recent studies propose third-order quasi-resonant interactions and associated modulational instabilities 11,12 inherent to the Nonlinear Schrödinger (NLS) equation as mechanisms for rogue wave formation 3,8,13–15. Such nonlinear effects cause the statistics of weakly nonlinear gravity waves to significantly differ from the Gaussian structure of linear seas, especially in long-crested or unidirectional (1D) seas 8,10,16–19. The late-stage evolution of modulation instability leads to breathers that can cause large waves 13–15 , especially in 1D waves. Indeed, in this case energy is 'trapped' as in a long wave-guide. For small wave steepness and negligible dissipa-tion, quasi-resonant interactions are effective in reshaping the wave spectrum, inducing large breathers via non-linear focusing before wave breaking occurs 16,17,20,21. Consequently, breathers can be observed experimentally in 1D wave fields only at sufficiently small values of wave steepness 20–22. However, wave breaking is inevitable when the steepness becomes larger: 'breathers do not breathe' 23 and their amplification is smaller than that predicted by the NLS equation, in accord with theoretical studies 24 of the compact Zakharov equation 25,26 and numerical studies of the Euler equations 27,28. Typical oceanic wind seas are short-crested, or multidirectional wave fields. Hence, we expect that nonlinear focusing due to modulational effects is diminished since energy can spread directionally 16,18,29. Thus, modulation instabilities may play an insignificant role in the wave growth especially in finite water depth where they are further attenuated 30. Tayfun 31 presented an analysis of oceanic measurements from the North Sea. His results indicate that large waves (measured as a function of time at a given point) result from the constructive interference (focusing) of elementary waves with random amplitudes and phases enhanced by second-order non-resonant or bound non-linearities. Further, the surface statistics follow the Tayfun 32 distribution 32 in agreement with observations 9,10,31,33. This is confirmed by a recent data quality control and statistical analysis of single-point measurements from fixed sensors mounted on offshore platforms, the majority of which were recorded in the North Sea 34. The analysis of