Tracking Breather Dynamics in Irregular Sea State Conditions

Abstract

Breather solutions of the nonlinear Schrödinger equation (NLSE) are known to be considered as backbone models for extreme events in the ocean as well as in Kerr media. These exact determinisitic rogue wave (RW) prototypes on a regular background describe a wide-range of modulation instability configurations. Alternatively, oceanic or electromagnetic wave fields can be of chaotic nature and it is known that RWs may develop in such conditions as well. We report an experimental study confirming that extreme localizations in an irregular oceanic JONSWAP wave field can be tracked back to originate from exact NLSE breather solutions, such as the Peregrine breather. Numerical NLSE as well as modified NLSE simulations are both in good agreement with laboratory experiments and highlight the significance of universal weakly nonlinear evolution equations in the emergence as well as prediction of extreme events in nonlinear dispersive media.Ocean extreme waves, also referred to as freak or rogue waves (RWs), are known to appear without warning and having disastrous impact, in consequence of the substantial large wave heights these can reach [1,2]. Studies on RWs attracted the scientific interest recently due to the interdisciplinary nature of the modulation instability (MI) of weakly nonlinear waves [3][4][5] as well as for the sake of accurate modeling and prediction of these mysterious extremes [6][7][8][9]. Indeed, exact solutions of the nonlinear Schrödinger equation (NLSE) provide backbone models that can be used to describe RWs, providing therefore deterministic numerical and laboratory prototypes to reveal novel insights of MI [10]. Within the vast range of pulsating NLSE solutions on finite background, there is one prominent candidate that is known to have similar physical properties as ocean RWs, namely, the doubly-localized Peregrine breather (PB) [11,12]. Despite the fact that it is theoretically assumed that the modulation period of the PB is infinite, laboratory observations confirmed that a finite number of waves in the background is sufficient to initiate its dynamics in nonlinear dispersive media [13][14][15]. These observations also proved that extreme localizations can be indeed discussed by means of the NLSE, despite violation of the theoretical assumption of the wave field to be or remain narrow-banded.Based on this latest progress, it is reasonable to study the dynamics of breathers, assuming irregularity of the underlying wave field in order to quantify limitations of the approach and to enlarge the scope of possible applications such as in oceanography. In fact, ocean waves' motion can be narrow-banded, such as in the case of swell. However, when winds, currents and wave breaking are at play, the wave field may experience strong irregularities, a state that limits applicability of the NLSE. Nevertheless, recent laboratory experiments showed the persistence of the PB in the presence of strong wind [16] and therefore its physical robustness to perturbations. To the best of our knowledge, the emergence o...

Effect of local Peregrine soliton emergence on statistics of random waves in the one-dimensional focusing nonlinear Schrödinger equation

“…Presence of the PSs in the spatiotemporal evolution of the partially-coherent wave in the 1-D focusing NLS governed systems is an experimentally verified fact [27][28][29]. However, the modulation instability cannot be considered as a dominating mechanism in this case.…”

Breather Rogue Waves in Random Seas

“…Thus, the effectiveness of the PB for modeling rogue waves in random seas depends on whether it can persist in such situations. More recently, it is confirmed in both laboratory and by weakly nonlinear numerical simulations that the PB is able to persist in random seas [14], which means that the PB can also be adopted for modeling rogue waves in irregular seas. Subsequently, Klein, et al [15] successfully reproduced the New Year Wave in laboratory by embedding the PB into RBW, and good agreement was achieved.…”

Experiments on higher-order and degenerate Akhmediev breather-type rogue water waves

“…The experiments are in a very good agreement with the fully nonlinear BEM-based NWT2D simulations with a spatial resolution of 2.5 cm while NLS provides a solid predicting power to study these higher-order breathers in a given hydrodynamic environment. Future work will be devoted to studies of the limitations of the theory of higherorder ABs when applied to the water surface as well as their applicability to realistic oceanic conditions following an example of Chabchoub (2016). Furthermore, the choice of NWT2D resolution in the analysis of steep nonlinear waves needs further investigations.…”

“…When studying the MI in laboratory environments, it turns out that breather description can be very useful when considering the excitation of extreme events (Dudley et al 2009;Kibler et al 2010;Chabchoub et al 2011Chabchoub et al , 2014. Lately, it has been shown that breathers can indeed persist in sea state configurations (Chabchoub 2016), thus, proving its importance in the study of unidirectional extreme seas. Furthermore, recent studies also emphasized the significance of these pulsating solutions for sea keeping tests as well as for developing standards for ships and marine offshore structures (Bitner-Gregersen and Gramstad 2015).…”