Super rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations

The rogue wave solutions (rational multi-breathers) of the nonlinear Schrodinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation (MNLS) also known as the Dysthe equation. This numerical modelling allowed us to directly compare simulations with recent results of laboratory measurements in \cite{Chabchoub2012c}. In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.Comment: under revision in Physical Review

Numerical modeling of rogue waves in coastal waters

Spatio-temporal evolution of rogue waves measured in Taiwanese coastal waters is reconstructed by means of numerical simulations. Their lifetimes are up to 100 s. The time series used for reconstructions were measured at dimensionless depths within the range of <i>kh</i> = 1.3&ndash;4.0, where <i>k</i> is the wave number and <i>h</i> is the depth. All identified rogue waves are surprisingly weakly nonlinear. The variable-coefficient approximate evolution equations, which take into account the shoaling effect, allow us to analyze the abnormal wave evolution over non-uniform real coastal bathymetry. The shallowest simulated point is characterized by <i>kh</i> &approx; 0.7. The reconstruction reveals an interesting peculiarity of the coastal rogue events: though the mean wave amplitudes increase as waves travel onshore, rogue waves are likely to occur at deeper locations, but not closer to the coast

Strongly nonlinear steepening of long interfacial waves

International audienceThe transformation of nonlinear long internal waves in a two-layer fluid is studied in the Boussinesq and rigid-lid approximation. Explicit analytic formulation of the evolution equation in terms of the Riemann invariants allows us to obtain analytical results characterizing strongly nonlinear wave steepening, including the spectral evolution. Effects manifesting the action of high nonlinear corrections of the model are highlighted. It is shown, in particular, that the breaking points on the wave profile may shift from the zero-crossing level. The wave steepening happens in a different way if the density jump is placed near the middle of the water bulk: then the wave deformation is almost symmetrical and two phases appear where the wave breaks

Freak waves in 2005

International audienceInformation about freak wave events in the ocean reported by mass media and derived from personal observations in 2005 is collected and analysed. Nine cases are selected as true freak wave events from a total number of 27 mentioned. Besides rogue waves in the open sea, the problem of freak wave events on the shore is emphasized. These accidents are related to unexpected wave impact upon the coast and shore constructions or to sudden intensive flooding of the coast. Of the nine events considered reliable here, three events correspond to open-sea cases, while the six others occurred nearshore