Linear and nonlinear rogue wave statistics in the presence of random currents

Abstract A series of directly numerical simulations of potential Euler equation have been performed using high-order spectral (HOS) method, to investigate the nonlinear wave statistics and the probability of rogue wave occurrence in crossing sea states. Several typical crossing sea states in deep water with different wave steepness are chosen for the computations. The ensemble statistical properties for those crossing waves are measured, including the temporal evolution of directional and omnidirectional wave spectra, exceedance probability of wave crest amplitude, as well as the kurtosis and skewness of free surface elevations. Particular attention is paid to the correlation between kurtosis and rogue wave occurrence. Our numerical results suggest that the global wave steepness plays a significant role in the statistical properties of crossing seas. Results also show the dependence of rogue wave occurrence probability on the kurtosis of free surface elevations.

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The North Sea Andrea storm and numerical simulations

Natural Hazards and Earth System Science ◽

10.5194/nhess-14-1407-2014 ◽

2014 ◽

Vol 14 (6) ◽

pp. 1407-1415 ◽

Cited By ~ 18

Author(s):

E. M. Bitner-Gregersen ◽

L. Fernandez ◽

J. M. Lefèvre ◽

J. Monbaliu ◽

A. Toffoli

Keyword(s):

Numerical Simulations ◽

North Sea ◽

Rogue Wave ◽

Grid Point ◽

Wave Model ◽

Wave Statistics ◽

The North ◽

Nonlinear Phase ◽

Spectral Wave Model ◽

The North Sea

Abstract. A coupling of a spectral wave model with a nonlinear phase-resolving model is used to reconstruct the evolution of wave statistics during a storm crossing the North Sea on 8–9 November 2007. During this storm a rogue wave (named the Andrea wave) was recorded at the Ekofisk field. The wave has characteristics comparable to the well-known New Year wave measured by Statoil at the Draupner platform 1 January 1995. Hindcast data of the storm at the nearest grid point to the Ekofisk field are here applied as input to calculate the evolution of random realizations of the sea surface and its statistical properties. Numerical simulations are carried out using the Euler equations with a higher-order spectral method (HOSM). Results are compared with some characteristics of the Andrea wave record measured by the down-looking lasers at Ekofisk.

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Rogue wave statistics from a noise-like-pulse laser

Advanced Photonics ◽

10.1364/np.2014.nm3a.7 ◽

2014 ◽

Cited By ~ 1

Author(s):

Caroline Lecaplain ◽

Philippe Grelu

Keyword(s):

Pulse Laser ◽

Rogue Wave ◽

Wave Statistics

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On Hokusai's Great wave off Kanagawa : localization, linearity and a rogue wave in sub-Antarctic waters

Notes and Records the Royal Society journal of the history of science ◽

10.1098/rsnr.2012.0066 ◽

2013 ◽

Vol 67 (2) ◽

pp. 159-164 ◽

Cited By ~ 7

Author(s):

J. M. Dudley ◽

V. Sarano ◽

F. Dias

Keyword(s):

Nonlinear Wave ◽

Rogue Wave ◽

Open Ocean ◽

Two Dimensional ◽

Wave Dynamics ◽

Antarctic Waters ◽

Storm Wave ◽

Linear And Nonlinear

The Hokusai woodcut entitled The great wave off Kanagawa has been interpreted as an unusually large storm wave, likely to be classed as a rogue wave, and possibly generated from nonlinear wave dynamics (J. H. E. Cartwright and H. Nakamura, Notes Rec. R. Soc. 63 , 119–135 (2009)). In this paper, we present a complementary discussion of this hypothesis, discussing in particular how linear and nonlinear mechanisms can both contribute to the emergence of rogue wave events. By making reference to the Great wave 's simultaneous transverse and longitudinal localization, we show that the purely linear mechanism of directional focusing also predicts characteristics consistent with those of the Great wave . In addition, we discuss the properties of a particular rogue wave photographed on the open ocean in sub-Antarctic waters, which shows two-dimensional localization and breaking dynamics remarkably similar to Hokusai's depiction in the woodcut.

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