Physical mechanisms of the rogue wave phenomenon

Abstract

Abstract:A review of physical mechanisms of the rogue wave phenomenon is given. The data of marine observations as well as laboratory experiments are briefly discussed. They demonstrate that freak waves may appear in deep and shallow waters. Simple statistical analysis of the rogue wave probability based on the assumption of a Gaussian wave field is reproduced. In the context of water wave theories the probabilistic approach shows that numerical simulations of freak waves should be made for very long times on large spatial domains and large number of realizations. As linear models of freak waves the following mechanisms are considered: dispersion enhancement of transient wave groups, geometrical focusing in basins of variable depth, and wave-current interaction. Taking into account nonlinearity of the water waves, these mechanisms remain valid but should be modified. Also, the influence of the nonlinear modulational instability (BenjaminFeir instability) on the rogue wave occurence is discussed. Specific numerical simulations were performed in the framework of classical nonlinear evolution equations: the nonlinear Schrödinger equation, the Davey -Stewartson system, the Korteweg -de Vries equation, the Kadomtsev -Petviashvili equation, the Zakharov equation, and the fully nonlinear potential equations. Their results show the main features of the physical mechanisms of rogue wave phenomenon.

Numerical simulation of deterministic freak wave sequences and wave-structure interaction

“…There have been some assumptions on the generation mechanism of freak wave, such as linear dispersive focusing, wave-current interaction, bottom topography influence-wind force on free surface, self-focusing due to boundary instability, and nonlinear wave-wave interaction, and so on (Kharif and Pelinovsky 2003). Linear dispersive focusing model, which shows a good predictability through pre-defining the size and shape of an abnormal wave, has been widely used as an efficient method to reproduce freak wave in both numerical and experimental studies.…”

Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents

“…In conformity with this definition, RWs were detected in a photonic crystal fibre [12], in a multi-stable state of an erbium-doped fibre laser [15], in chaotic but deterministic regime of optical injected semiconductor lasers [5,8], in nonlinear optical cavity [11], in acoustic turbulence in He II [9] and other set-ups [13]. On the formation of the ocean RWs, a number of supporting theories have been developed [1][2][3][4]. Among various possible factors contributing to the creation of the RW, the modulation instability (MI) supported by the nonlinear effect is believed to play a crucial role, by inducing preliminary amplification of water wave height, which may trigger self-attractive nonlinear interaction, initiating the RW formation [20].…”

“…The higher rational solutions having free parameters [26,27] become parameterless for a single-peak RW solution [27]. On the other hand, in our two-dimensional RW model the maximum amplitude A rog (c) can be varied continuously and increased as required, by tuning an arbitrary parameter c in the same single-peak, first-order solution (3.1) or its dynamical extension (3.8) (as shown in figure 4a-d), making the model suitable for RWs with a diverse range of heights, anywhere in the range 17-30 m in calm sea [1][2][3][4][5][6], as observed in deep-sea two-dimensional RWs.…”

“…The mysterious ocean rogue waves (RWs) are reported to be observed in a relatively calm sea, where they, as a localized and isolated surface waves, apparently appear from nowhere, make a sudden hole in the sea just before attaining surprisingly high amplitude and disappear again without a trace ( [1][2][3][4][5][6][7], http://news.bbc.co.uk/2/hi/8548547.stm). This elusive freak wave caught the imagination of the broad scientific community quite recently [8][9][10][11][12][13][14][15], triggering off an upsurge in theoretical [7,[16][17][18] and experimental [5,[8][9][10][11][12][13][14][15] studies of this unique phenomenon.…”

Systematic study of rogue wave probability distributions in a fourth‐order nonlinear Schrödinger equation

“…[3] The scientific community has studied the topic experimentally (in water tanks) [Onorato et al, 2004[Onorato et al, , 2006, observationally (with satellite imaging, for example) [Dankert et al, 2003;Schulz-Stellenfleth and Lehner, 2004], and theoretically [Kharif and Pelinovsky, 2003]. A review of recent progress in freak wave forecasting can be found in an article by Dysthe et al [2008].…”