2001
DOI: 10.1103/physrevlett.86.5831
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Freak Waves in Random Oceanic Sea States

Abstract: Freak waves are very large, rare events in a random ocean wave train. Here we study the numerical generation of freak waves in a random sea state characterized by the JONSWAP power spectrum. We assume, to cubic order in nonlinearity, that the wave dynamics are governed by the nonlinear Schroedinger (NLS) equation. We identify two parameters in the power spectrum that control the nonlinear dynamics: the Phillips parameter α and the enhancement coefficient γ. We discuss how freak waves in a random sea state are … Show more

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Cited by 501 publications
(372 citation statements)
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“…In the most part of previous investigations, however, breathers were created within the background wave field by mean of properly devised setups, and little is known about their likelihood to emerge spontaneously in random sea states. Remarkably, this important aspect of the problem has been addressed only in a few instances [24,23,30] and limited to the framework of the NLS equation. We also note that, in order to shed light on the structures embedded in a random sea, it is necessary to follow the evolution of wave groups over large spatial and temporal scales jointly.…”
Section: Introductionmentioning
confidence: 99%
“…In the most part of previous investigations, however, breathers were created within the background wave field by mean of properly devised setups, and little is known about their likelihood to emerge spontaneously in random sea states. Remarkably, this important aspect of the problem has been addressed only in a few instances [24,23,30] and limited to the framework of the NLS equation. We also note that, in order to shed light on the structures embedded in a random sea, it is necessary to follow the evolution of wave groups over large spatial and temporal scales jointly.…”
Section: Introductionmentioning
confidence: 99%
“…The main objective of the present work is to demonstrate the existence of the collision process of Akhmediev breathers in real physical systems, so complete control of all the physical parameters is required in the first phase, which prevents any statistical analysis. It is still of fundamental importance to consider the coherent and deterministic approach to the understanding of rogue-wave phenomena in realistic oceanic conditions [17,18]. A recent work has investigated the interaction between waves and ships during extreme ocean conditions using such breather solutions [19].…”
Section: Introductionmentioning
confidence: 99%
“…This equation is a prototypical dispersive nonlinear partial differential equation that has been central for almost four decades now to a variety of areas in Mathematical Physics. The relevant fields of application may vary from optics and propagation of the electric field in optical fibers (Hasegawa and Kodama [20], Malomed [27]), to the self-focusing and collapse of Langmuir waves in plasma physics (Zakharov [40]) and the behaviour of deep water waves and freak waves (the so-called rogue waves) in the ocean (Benjamin and Feir [5] and Onorato, Osborne, Serio and Bertone [32]). The nonlinear Schrödinger equation also describes various phenomena arising in: self-channelling of a highpower ultra-short laser in matter, in the theory of Heisenberg ferromagnets and magnons, in dissipative quantum mechanics, in condensed matter theory, in plasma physics (e.g., the Kurihara superfluid film equation).…”
Section: Introduction and Auxiliary Resultsmentioning
confidence: 99%