Nonlinear Fourier classification of 663 rogue waves measured in the Philippine Sea.

Rogue waves are sudden and extreme occurrences, with heights that exceed twice the significant wave height of their neighboring 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. Recently, nonlinear Fourier transforms (NFTs), which generalize the usual Fourier transform, have been leveraged to analyze oceanic rogue waves. Next to the usual linear Fourier modes, NFTs can additionally uncover nonlinear Fourier modes in time series that are usually hidden. However, so far only individual oceanic rogue waves have been analyzed using NFTs in the literature. Moreover, the completely different types of nonlinear Fourier modes have been observed in these studies. Exploiting twelve years of field measurement data from an ocean buoy, we apply the nonlinear Fourier transform (NFT) for the nonlinear Schrödinger equation (NLSE) (referred to 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 of deep-water rogue waves. We categorize the measured rogue waves into four types based on the characteristics of the largest nonlinear mode: stable, small breather, large breather and (envelope) soliton. We find that all types can occur at a single site, and investigate which conditions are dominated by a single type at the measurement site. The one and two-dimensional Benjamin-Feir indices (BFIs) are employed to examine the four types of nonlinear spectra. Furthermore, we verify on a part of the data set that for the localized types, the largest nonlinear Fourier mode can be attributed directly to the rogue wave, and investigate the relation between the height of the rogue waves and that of the dominant nonlinear Fourier mode. While the dominant nonlinear Fourier mode in general only contributes a small fraction of the rogue wave, we find that soliton modes can contribute up to half of the rogue wave. Since the NLSE does not account for directional spreading, the classification is repeated for the first quartile with the lowest directional spreading for each type. Similar results are obtained.

Large-scale experiments into the tsunamigenic potential of different iceberg calving mechanisms.

Mass balance analysis of ice sheets is a key component to understand the effects of global warming. A significant component of ice sheet and shelf mass balance is iceberg calving, which can generate large tsunamis endangering human beings and coastal infrastructure. Such iceberg-tsunamis have reached amplitudes of 50 m and destroyed harbours. Calving icebergs interact with the surrounding water through different mechanisms and we investigate five; A: capsizing, B: gravity-dominated fall, C: buoyancy-dominated fall, D: gravity-dominated overturning and E: buoyancy-dominated overturning. Gravity-dominated icebergs essentially fall into the water body whereas buoyancy-dominated icebergs rise to the water surface. We find with unique large-scale laboratory experiments that iceberg-tsunami heights from gravity-dominated mechanisms (B and D) are roughly an order of magnitude larger than from A, C and E. A theoretical model for released iceberg energy supports this finding and the measured wave periods upscaled to Greenlandic outlet glaciers agree with field observations. Whilst existing empirical equations for landslide-tsunamis establish estimates of an upper envelope of the maximum iceberg-tsunami heights, they fail to capture the physics of most iceberg-tsunami mechanisms.