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.

A σ-coordinate non-hydrostatic model with embedded Boussinesq-type-like equations for modeling deep-water waves

Abstract: A σ-coordinate non-hydrostatic model, combined with the embedded Boussinesq-type-like equations, a reference velocity, and an adapted top-layer control, is developed to study the evolution of deep-water waves. The advantage of using the Boussinesq-type-like equations with the reference velocity is to provide an analytical-based non-hydrostatic pressure distribution at the top-layer and to optimize wave dispersion property. The σ-based non-hydrostatic model naturally tackles the so-called overshooting issue in the case of non-linear steep waves. Efficiency and accuracy of this non-hydrostatic model in terms of wave dispersion and nonlinearity are critically examined. Overall results show that the newly developed model using a few layers is capable of resolving the evolution of non-linear deep-water wave groups. Copyright © 2009 John Wiley & Sons, Ltd.

Linear and Nonlinear Rogue Wave Statistics in the Presence of Random Currents

Abstract: We review recent progress in modeling the probability distribution of wave heights in the deep ocean as a function of a small number of parameters describing the local sea state. Both linear and nonlinear mechanisms of rogue wave formation are considered. First, we show that when the average wave steepness is small and nonlinear wave effects are subleading, the wave height distribution is well explained by a single "freak index" parameter, which describes the strength of (linear) wave scattering by random currents relative to the angular spread of the incoming random sea. When the average steepness is large, the wave height distribution takes a very similar functional form, but the key variables determining the probability distribution are the steepness, and the angular and frequency spread of the incoming waves. Finally, even greater probability of extreme wave formation is predicted when linear and nonlinear effects are acting together.

General rogue waves in the three-wave resonant interaction systems

Abstract: General rogue waves in (1+1)-dimensional three-wave resonant interaction systems are derived by the bilinear method. These solutions are divided into three families, which correspond to a simple root, two simple roots and a double root of a certain quartic equation arising from the dimension reduction respectively. It is shown that while the first family of solutions associated with a simple root exist for all signs of the nonlinear coefficients in the three-wave interaction equations, the other two families of solutions associated with two simple roots and a double root can only exist in the so-called soliton-exchange case, where the nonlinear coefficients have certain signs. Many of these rogue wave solutions, such as those associated with two simple roots, and higher-order solutions associated with a simple root, are new solutions which have not been reported before. Technically, our bilinear derivation of rogue waves for the double-root case is achieved by a generalization to the previous dimension reduction procedure in the bilinear method, and this generalized procedure allows us to treat roots of arbitrary multiplicities. Dynamics of the derived rogue waves is also examined, and new rogue-wave patterns are presented. Connection between these bilinear rogue waves and those derived earlier by Darboux transformation is also explained.