Rogue wave

About: Rogue wave is a research topic. Over the lifetime, 2977 publications have been published within this topic receiving 70933 citations. The topic is also known as: freak wave & monster wave.

On the highest non-breaking wave in a group: fully nonlinear water wave breathers versus weakly nonlinear theory

Abstract: In nature, water waves usually propagate in groups and the open question about the characteristics of the highest possible wave in a group is of significant theoretical and practical interest. We examine the problem of the highest non-breaking wave in a wave group by direct numerical simulations of the exact Euler equations. The main aim of the study is twofold: (i) to describe the highest wave in a group in fully nonlinear setting and find its dependence on parameters; (ii) to examine correspondence between the exact breather solutions of weakly nonlinear analytic theory based on the integrable nonlinear Schrodinger (NLS) equation and their strongly nonlinear analogues. In contrast to weakly nonlinear models the very notion of the highest wave is ill-defined: the maximal crest elevation, the maximal trough-to-crest height and the deepest trough all occur at close but different moments; correspondingly, we have to speak about distinctively different extreme waves. In the simulations small initial perturbation of a uniform wave train were prescribed in a way ensuring that the initial perturbation excites a single breather-type modulation. The ensuing growth results in higher wave magnitudes and takes longer time to develop compared with the NLS theory. The maxima of crest elevation noticeably exceed their weakly nonlinear analogues. The wave with the highest crest differs significantly from the unmodulated wave: the local wavelength contracts considerably, the crest becomes noticeably higher; the vicinity of the crest of such an extreme wave is close to that of the limiting Stokes periodic wave. Thus, the shape of the maximal crest wave is almost universal, i.e. it practically does not depend on the way the wave group evolved, or even whether there was initially more than one group. The evolution of a single NLS breather has been shown to have a qualitatively similar but quantitatively quite different analogue in the fully nonlinear setting. The one-to-one mapping of the NLS breather solutions onto fully nonlinear ones has been constructed. The fully nonlinear breathers are found to be robust, which provides grounds for applying the results for developing short-term deterministic forecasting of rogue waves.

Characteristics of the breathers, rogue waves and solitary waves in a generalized (2+1)-dimensional Boussinesq equation

Abstract: Under investigation in this work is a generalized (2+1)-dimensional Boussinesq equation, which can be used to describe the propagation of small-amplitude, long wave in shallow water. By virtue of Bell's polynomials, an effective way is presented to succinctly construct its bilinear form. Furthermore, based on the bilinear formalism and the extended homoclinic test method, the breather wave solution, rogue-wave solution and solitary-wave solution of the equation are well constructed. Our results can be used to enrich the dynamical behavior of the generalized (2+1)-dimensional nonlinear wave fields.

Rogue waves of the Kundu-Eckhaus equation in a chaotic wave field

Abstract: In this paper we study the properties of the chaotic wave fields generated in the frame of the Kundu-Eckhaus equation (KEE). Modulation instability results in a chaotic wave field which exhibits small-scale filaments with a free propagation constant, $k$. The average velocity of the filaments is approximately given by the average group velocity calculated from the dispersion relation for the plane-wave solution; however, direction of propagation is controlled by the $\ensuremath{\beta}$ parameter, the constant in front of the Raman-effect term. We have also calculated the probabilities of the rogue wave occurrence for various values of propagation constant $k$ and showed that the probability of rogue wave occurrence depends on $k$. Additionally, we have showed that the probability of rogue wave occurrence significantly depends on the quintic and the Raman-effect nonlinear terms of the KEE. Statistical comparisons between the KEE and the cubic nonlinear Schr\"odinger equation have also been presented.