Topic
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.
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TL;DR: This analysis reveals the existence of rogue wave clusters with a high level of symmetry in the (x,t) plane that arise naturally when the shifts in the Darboux scheme are taken to be eigenvalue dependent.
Abstract: Using the Darboux transformation technique and numerical simulations, we study the hierarchy of rational solutions of the nonlinear Schrodinger equation that can be considered as higher order rogue waves in this model. This analysis reveals the existence of rogue wave clusters with a high level of symmetry in the (x,t) plane. These structures arise naturally when the shifts in the Darboux scheme are taken to be eigenvalue dependent. We have found single-shell structures where a central higher order rogue wave is surrounded by a ring of first order peaks on the (x,t) plane.
189 citations
TL;DR: Recent numerical and experimental data suggest that the probability of the appearance of rogue waves in a chaotic wave state in such systems increases when the initial state is a random function of sufficiently high amplitude.
Abstract: Turbulence in dynamical systems is one of the most intriguing phenomena of modern science. Integrable systems offer the possibility to understand, to some extent, turbulence. Recent numerical and experimental data suggest that the probability of the appearance of rogue waves in a chaotic wave state in such systems increases when the initial state is a random function of sufficiently high amplitude. We provide explanations for this effect.
188 citations
TL;DR: Microwave transport experiments have been performed in a quasi-two-dimensional resonator with randomly distributed conical scatterers with branching structures similar to those observed in stationary imaging of electron flow, which confirm that caustics in the ray dynamics are responsible for these structures.
Abstract: Microwave transport experiments have been performed in a quasi-two-dimensional resonator with randomly distributed conical scatterers. At high frequencies, the flow shows branching structures similar to those observed in stationary imaging of electron flow. Semiclassical simulations confirm that caustics in the ray dynamics are responsible for these structures. At lower frequencies, large deviations from Rayleigh's law for the wave height distribution are observed, which can only partially be described by existing multiple-scattering theories. In particular, there are "hot spots" with intensities far beyond those expected in a random wave field. The results are analogous to flow patterns observed in the ocean in the presence of spatially varying currents or depth variations in the sea floor, where branches and hot spots lead to an enhanced frequency of freak or rogue wave formation.
188 citations
TL;DR: A novel family of analytic solutions of the three-wave resonant interaction equations for the purpose of modeling unique events, i.e., "amplitude peaks" which are isolated in space and time are introduced.
Abstract: We introduce a novel family of analytic solutions of the three-wave resonant interaction equations for the purpose of modeling unique events, i.e., "amplitude peaks" which are isolated in space and time. The description of these solutions is likely to be a crucial step in the understanding and forecasting of rogue waves in a variety of multicomponent wave dynamics, from oceanography to optics and from plasma physics to acoustics.
188 citations
TL;DR: This work analyzes several sets of field data in various European locations with various tools, and finds that the main generation mechanism for rogue waves is the constructive interference of elementary waves enhanced by second-order bound nonlinearities and not the modulational instability.
Abstract: Since the 1990s, the modulational instability has commonly been used to explain the occurrence of rogue waves that appear from nowhere in the open ocean. However, the importance of this instability in the context of ocean waves is not well established. This mechanism has been successfully studied in laboratory experiments and in mathematical studies, but there is no consensus on what actually takes place in the ocean. In this work, we question the oceanic relevance of this paradigm. In particular, we analyze several sets of field data in various European locations with various tools, and find that the main generation mechanism for rogue waves is the constructive interference of elementary waves enhanced by second-order bound nonlinearities and not the modulational instability. This implies that rogue waves are likely to be rare occurrences of weakly nonlinear random seas.
185 citations