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

Abstract

A possible mechanism that is responsible for the occurrence of rogue waves in the ocean is the Benjamin-Feir instability or modulation instability. The deterministic framework that describes this latter instability of Stokes waves in deep water is provided by the family of Akhmediev breather (AB) solutions of the nonlinear Schrödinger equation (NLS). It is indeed very convenient to use these exact pulsating envelopes particularly for laboratory experiments, since they allow to generate extreme waves at any location in space at any instant of time. As such, using this framework is more advantageous compared to the classical initialization of the unstable wave dynamics from a three wave system (main wave frequency and one pair of unstable sidebands). In this work, we report an experimental study on higher-order AB hydrodynamics that describe a higher-order stage of modulation instability, namely, starting from five wave systems (main wave frequency and two pairs of unstable sidebands). The corresponding laboratory experiments, that have been conducted in a large water wave facility, confirm the NLS wave dynamics forecast while boundary element method-

Experimental Realization of Periodic Deep-Water Wave Envelopes with and without Dissipation

“…This type of wave behaviour has been observed earlier [8]; however, it has been attributed to the fact that DN-type envelopes do not describe a stable and relevant physical wave pattern as suggested by the NLS theory. Further studies will be devoted to understand the observed phenomena quantitavely [22], using, for instance, more accurate hydrodynamic numerical schemes, such as the higher-order spectral method [23] or the boundary element method [24]. Further studies will be conducted to understand the intrinsic manifold behaviour of the CN and DN solutions in the presence of dissipation and to clarify the formation of extreme events on such periodic wave envelope configurations [6,7].…”

Foreword to special issue on Rogue Waves

“…Good agreement between the experimental results and numerical simulations is obtained. On the other hand, Chabchoub et al (2017) present results from experimental study describing higher order stage of modulation instability, starting from five-wave systems (main wave frequency and two pairs of unstable sidebands). Laboratory data confirm the NLS wave dynamics forecast by Akhmediev breather solutions.…”

Novel nonlinear wave equation: Regulated rogue waves and accelerated soliton solutions

“…Such sudden and steep isolated waves with a single peak, borrowing the concept from the deep oceanic waves, are causing upsurge of theoretical and experimental studies in various fields [4]- [14]. Such phenomena can be modelled by RW solutions defined in (1+1) space-time dimensions.…”

“…Such RWs unlike usual soliton solutions grow in amplitudes while moving reaching to its maximum at certain time and disappearing again to the background waves. However in spite of its generic nature and success in explaining RW phenomena in experimental observations in diverse fields [8][9][10][11][12][13][14], the description of RW by Peregrine breather is limited to a fixed maximum amplitude (3 times of background wave) and fixed RW width. This is due to the absence of any free parameters in Peregrine RW solutions [4].…”