Refraction of a Gaussian seaway

Abstract

[1] Refraction of a Longuet-Higgins Gaussian sea by random ocean currents creates persistent local variations (in the form of lumps or streaks) in average energy and wave action distributions. These variations explicitly survive averaging over wavelength and wave propagation direction. The lumps and streaks in average local action mean that the uniform sampling assumed in the venerable Longuet-Higgins theory does not apply. Proper handling of the nonuniform sampling results in greatly increased probability of freak wave formation. The present theory represents a synthesis of Longuet-Higgins Gaussian seas and the refraction model of White and Fornberg, which used a nonGaussian nonstatistical plane wave incident seaway. Using the linearized equations for deep ocean waves, we obtain quantitative predictions for the increased probability of freak wave formation when the refractive effects are taken into account. The wave height distribution depends primarily on the ''freak index,'' g, which measures the strength of refraction relative to the angular spread of the incoming sea. Dramatic effects are obtained in the tail of this distribution even for the modest values of the freak index that are expected to occur commonly in nature. Extensive comparisons are made between the analytical description and numerical simulations.

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

“…After fully understanding the quantitative consequences of the nonlinear effect, the ultimate goal of the project is to combine nonlinearity and deflection by random currents in a single model, which will allow the probability of rogue wave formation to be predicted for a wide range of realistic sea conditions. Previous linear results show that the effect of current is well characterized by a single parameter: the freak index [Heller et al, 2008;Ying et al, 2011]. Preliminary results of combining nonlinearity and deflection by Figure 10.…”

“…These studies suggest that the interaction between incoming wave and current may serve as a triggering mechanism for the formation of freak waves during nonlinear wave evolution. In the work by Heller et al [2008], a freak index is defined in terms of the mean wave speed, mean current speed, and the angular spread of the incoming wave, and a quantitative relationship is predicted between this freak index and the occurrence probability of freak waves. However, in this work ray dynamics is used in place of the real wave equation for ocean waves, and nonlinearity is not included in the model.…”

“…[9] The effect of currents interacting with an incoming sea state has been studied by Heller et al [2008] using ray dynamics and by Janssen and Herbers [2009] using Monte Carlo simulations. These studies suggest that the interaction between incoming wave and current may serve as a triggering mechanism for the formation of freak waves during nonlinear wave evolution.…”

Extreme events in complex linear and nonlinear photonic media

“…Numerous naval disasters leading to ship disappearance under uncertain conditions have been attributed to these waves. Since sailors are well known story makers these monster, destructive waves that were in naval folklore perhaps for thousands of years penetrated the realm of science only recently and after quantitative observations [1,2]. Since then, they seem to spring up in many other fields including optics [3][4][5][6][7], BEC and matter waves, finance, etc [8][9][10][11][12].…”

“…Intuitively, one may link the onset of a rogue wave to a resonant interaction of two or three solitary waves that may appear in the medium. However, large amplitude events may also appear in a purely linear regime [1,2,4,6]; a typical example is the generation of caustic surfaces in wave propagation [13,14].Propagation of electrons or light in a weakly scattering medium is a well-studied classical problem related to Anderson localization and caustic formation. Recent experiments in the optical regime [15] have shown clearly both the theoretically predicted light localization features as well as the localizing role of (focusing) nonlinearity in the propagation [15][16][17][18][19][20].…”