Generation mechanism and prediction of an observed extreme rogue wave

Johannes Gemmrich,Leah Cicon

doi:10.1038/s41598-022-05671-4

Abstract

Rogue waves are individual ocean surface waves with crest height eta or trough-to-crest height H that are large compared to the significant wave height H_s of the underlying sea state: H/H_s>2.2 or eta /H_s>1.25. The physics of rogue wave generation and the potential of predicting the rogue wave risk are open questions. Only a few rogue waves in high sea states have been observed directly, but they can pose a danger to marine operations, onshore and offshore structures, and beachgoers. Here we report on a 17.6m high rogue wave in coastal waters with eta /H_s=1.98 and H/H_s=2.9 which are likely the largest normalized heights ever recorded. Simulations of random superposition of Stokes waves in intermediate water depth show good agreement with the observation. Non-linear wave modulational instability, a well known cause for rogue waves in laboratory settings, did not contribute significantly to the rogue wave generation. A parameter obtained from a routine spectral wave forecast provides a practical risk prediction for rogue waves. These results confirm that probabilistic prediction of oceanic rogue waves based on random superposition of steep waves are possible and should replace predictions based on modulational instability.

Highlights

Rogue waves are individual ocean surface waves with crest height η or trough-to-crest height H that are large compared to the significant wave height Hs of the underlying sea state: H/Hs > 2.2 or η/Hs > 1.25
The sea is a random superposition of linear waves of a narrow frequency spectrum and the individual wave heights H follow the Rayleigh d istribution[11]
Observations from the GORM platform in the North Sea showed that the distribution of moderate wave heights H/Hs 2 is consistent with second order models accounting for finite spectral bandwidth, but extreme waves H/Hs ≫ 2 seem to follow a different d istribution[9]

Summary

Introduction

Rogue waves are individual ocean surface waves with crest height η or trough-to-crest height H that are large compared to the significant wave height Hs of the underlying sea state: H/Hs > 2.2 or η/Hs > 1.25. Observations from the GORM platform in the North Sea showed that the distribution of moderate wave heights H/Hs 2 is consistent with second order models accounting for finite spectral bandwidth, but extreme waves H/Hs ≫ 2 seem to follow a different d istribution[9]. Under modulational instability the tails of the probability density function of wave crests and wave heights will be higher than predicted by second order theory. MonteCarlo simulation of random superposition of fourth order Stokes waves[8] drawn from the observed wave energy spectra yield wave and crest height distributions in good agreement with the 10 month buoy record, including the extreme rogue wave. We show that the crest-trough correlation r25–27 calculated from a WAVEWATCH III®28 (WW3) wave model has strong predictive power for rogue wave risk prediction from a standard wave forecast model

Methods

Findings

Conclusion