Nonlinear Four-Wave Interactions and Freak Waves

By Peter A. E. M. Janssen. 2003

786 citations recorded by the source corpus.

Subfields: Atmospheric Science, Earth-Surface Processes, Oceanography

View Paper: https://www.semanticscholar.org/paper/57b782745b657249e41a527e8fd2435f4e825772

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Citations in the corpus

Physical Mechanisms of the Rogue Wave Phenomenon (2003, methodology): “Very recently, Janssen [81] developed a kinetic equation from the Zakharov equation including quasi-resonances.”
On Kurtosis and Occurrence Probability of Freak Waves (2006, methodology): “where, for brevity, we have introduced the notation b1 b(k1), and so on, and the nonlinear transfer function T1,2,3,4 as found by Krasitskii (1990) enjoys a number of symmetries that guarantee that the Zakharov equation is Hamiltonian and conserves wave energy.”
Extreme Ocean Waves (2008, background): “In a random sea state, this results in strong deviations from Gaussian-and secondorder-based statistics (Janssen 2003; Onorato et al. 2001, 2006b; Mori and Yasuda 2002; Mori et al. 2007; Socquet-Juglard et al. 2005; Trulsen and Dysthe 1997; Mori and Janssen 2006; Toffoli et al. 2009).”
Rogue waves and their generating mechanisms in different physical contexts (2013, methodology): “Indeed, it has been shown in [41] that quasi-resonant interaction between free modes may result in an increase (in deep water) or a decrease”
Optical wave turbulence: Towards a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics (2014, neutral): “It is important to note that similar generalizations of the WT kinetic equation were originally developed in the context of hydrodynamic waves (see [391] for a review), and are still important when one considers the early stage of the evolution of the turbulent system, see, e.”
An efficient model for three-dimensional surface wave simulations (2005, methodology): “The effect of nonlinear four-wave interactions on the formation of freak waves was studied by Janssen [21] using the NLS and the Zakharov equations.”
What makes the Peregrine soliton so special as a prototype of freak waves? (2010, positive): “The criterion specifying when the modulational instability persists for narrow-band random wave fields was found and on its basis Janssen [13] introduced the Benjamin–Feir Index (BFI) to characterize the narrowness of the wind-wave spectra (more precisely the ratio of nonlinear and dispersion effect”