Author

# Kristian B. Dysthe

Other affiliations: University of Tromsø, University of Oslo

Bio: Kristian B. Dysthe is an academic researcher from University of Bergen. The author has contributed to research in topics: Wind wave & Nonlinear system. The author has an hindex of 17, co-authored 34 publications receiving 2280 citations. Previous affiliations of Kristian B. Dysthe include University of Tromsø & University of Oslo.

Topics: Wind wave, Nonlinear system, Breaking wave, Rogue wave, Gravity wave

##### Papers

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TL;DR: In most circumstances, the properties of rogue waves and their probability of occurrence appear to be consistent with second-order random-wave theory as mentioned in this paper, although it is unclear whether these represent measurement errors or statistical flukes, or are caused by physical mechanisms not covered by the model.

Abstract: Oceanic rogue waves are surface gravity waves whose wave heights are much larger than expected for the sea state. The common operational definition requires them to be at least twice as large as the significant wave height. In most circumstances, the properties of rogue waves and their probability of occurrence appear to be consistent with second-order random-wave theory. There are exceptions, although it is unclear whether these represent measurement errors or statistical flukes, or are caused by physical mechanisms not covered by the model. A clear deviation from second-order theory occurs in numerical simulations and wave-tank experiments, in which a higher frequency of occurrence of rogue waves is found in long-crested waves owing to a nonlinear instability.

777 citations

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TL;DR: In this paper, the authors take a closer look on these simple solutions and compare them with some of the simulation data (Henderson et al to appear in Wave Motion) and find that the Ma breather and Peregrine solution may provide useful and simple analytical models for 'freak' wave events.

Abstract: Some breather type solutions of the NLS equation have been suggested by Henderson et al (to appear in Wave Motion) as models for a class of 'freak' wave events seen in 2D-simulations on surface gravity waves. In this paper we first take a closer look on these simple solutions and compare them with some of the simulation data (Henderson et al to appear in Wave Motion). Our findings tend to strengthen the idea of Henderson et al. Especially the Ma breather and the so called Peregrine solution may provide useful and simple analytical models for 'freak' wave events.

339 citations

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TL;DR: In this article, the modified nonlinear Schrodinger equation of Dysthe is extended by relaxing the narrow bandwidth constraint to make it more suitable for application to a realistic ocean wave spectrum.

270 citations

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TL;DR: In this paper, the authors performed simulations with a fairly narrow band numerical gravity wave model (higher-order NLS type) and a computational domain of dimensions 128 x 128 typical wavelengths, and found that the probability distributions of surface elevation and crest height are found to fit theoretical distributions found by Tayfun (J. Geophys. Res. vol.

Abstract: Simulations have been performed with a fairly narrow band numerical gravity wave model (higher-order NLS type) and a computational domain of dimensions 128 x 128 typical wavelengths. The simulations are initiated with ∼ 6 x 10 4 Fourier modes corresponding to truncated JONSWAP spectra and different angular distributions giving both short- and long-crested waves. A development of the spectra on the so-called Benjamin-Feir timescale is seen, similar to the one reported by Dysthe et al. (J. Fluid Mech. vol. 478, 2003, p. 1). The probability distributions of surface elevation and crest height are found to fit theoretical distributions found by Tayfun (J. Geophys. Res. vol. 85, 1980, p. 1548) very well for elevations up to four standard deviations (for realistic angular spectral distributions). Moreover, in this range of the distributions, the influence of the spectral evolution seems insignificant. For the extreme parts of the distributions a significant correlation with the spectral change can be seen for very long-crested waves. For this case we find that the density of large waves increases during spectral change, in agreement with a recent experimental study by Onorato et al. (J. Fluid Mech. 2004 submitted).

250 citations

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TL;DR: In this paper, a truncated amplitude equation with exact linear dispersion was proposed for modeling weakly nonlinear waves, based on the nonlinear Schrodinger (NLS) equation for deep-water waves.

Abstract: We propose a new approach for modeling weakly nonlinear waves, based on enhancing truncated amplitude equations with exact linear dispersion. Our example is based on the nonlinear Schrodinger (NLS) equation for deep-water waves. The enhanced NLS equation reproduces exactly the conditions for nonlinear four-wave resonance (the “figure 8” of Phillips) even for bandwidths greater than unity. Sideband instability for uniform Stokes waves is limited to finite bandwidths only, and agrees well with exact results of McLean; therefore, sideband instability cannot produce energy leakage to high-wave-number modes for the enhanced equation, as reported previously for the NLS equation. The new equation is extractable from the Zakharov integral equation, and can be regarded as an intermediate between the latter and the NLS equation. Being solvable numerically at no additional cost in comparison with the NLS equation, the new model is physically and numerically attractive for investigation of wave evolution.

181 citations

##### Cited by

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TL;DR: To the best of our knowledge, there is only one application of mathematical modelling to face recognition as mentioned in this paper, and it is a face recognition problem that scarcely clamoured for attention before the computer age but, having surfaced, has attracted the attention of some fine minds.

Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

3,015 citations

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TL;DR: This work reports the observation of rogue waves in an optical system, based on a microstructured optical fibre, near the threshold of soliton-fission supercontinuum generation—a noise-sensitive nonlinear process in which extremely broadband radiation is generated from a narrowband input.

Abstract: Recent observations show that the probability of encountering an extremely large rogue wave in the open ocean is much larger than expected from ordinary wave-amplitude statistics. Although considerable effort has been directed towards understanding the physics behind these mysterious and potentially destructive events, the complete picture remains uncertain. Furthermore, rogue waves have not yet been observed in other physical systems. Here, we introduce the concept of optical rogue waves, a counterpart of the infamous rare water waves. Using a new real-time detection technique, we study a system that exposes extremely steep, large waves as rare outcomes from an almost identically prepared initial population of waves. Specifically, we report the observation of rogue waves in an optical system, based on a microstructured optical fibre, near the threshold of soliton-fission supercontinuum generation--a noise-sensitive nonlinear process in which extremely broadband radiation is generated from a narrowband input. We model the generation of these rogue waves using the generalized nonlinear Schrodinger equation and demonstrate that they arise infrequently from initially smooth pulses owing to power transfer seeded by a small noise perturbation.

2,173 citations

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TL;DR: In this paper, Hilbert spectral analysis is proposed as an alternative to wavelet analysis, which provides not only a more precise definition of particular events in time-frequency space, but also more physically meaningful interpretations of the underlying dynamic processes.

Abstract: We survey the newly developed Hilbert spectral analysis method and its applications to Stokes waves, nonlinear wave evolution processes, the spectral form of the random wave field, and turbulence. Our emphasis is on the inadequacy of presently available methods in nonlinear and nonstationary data analysis. Hilbert spectral analysis is here proposed as an alternative. This new method provides not only a more precise definition of particular events in time-frequency space than wavelet analysis, but also more physically meaningful interpretations of the underlying dynamic processes.

1,945 citations

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TL;DR: The Peregrine soliton was observed experimentally for the first time by using femtosecond pulses in an optical fiber as mentioned in this paper, which gave some insight into freak waves that can appear out of nowhere before simply disappearing.

Abstract: The Peregrine soliton — a wave localized in both space and time — is now observed experimentally for the first time by using femtosecond pulses in an optical fibre. The results give some insight into freak waves that can appear out of nowhere before simply disappearing.

1,158 citations

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TL;DR: In this article, a hierarchy of rational solutions of the nonlinear Schrodinger equation (NLSE) with increasing order and with progressively increasing amplitude is presented. And the authors apply the WANDT title to two objects: rogue waves in the ocean and rational solution of the NLSE.

1,036 citations