No abstract

Wave fields for near homoclinic, single mode rogue-wave solutions of the periodic nonlinear Schrödinger equation are presented. Parameters of candidate solutions are estimated and refined through an eigenvalue solution procedure. An overview of the estimation and refining procedure used by the authors is provided. Solutions are scaled to facilitate experimental implementation. The continuous wavelet transform is used to carry out time-frequency analyses and the results obtained are demonstrative of the dispersion relation as well as the time varying side band energy transfer associated with the Benjamin-Feir instability. The analysis framework and approach used are validated with the Peregrine solution. Other extreme wave solutions are analyzed as well. The framework presented here could serve as a basis for experimental investigations into single mode rogue waves as well as other localizations in wave fields.

Smoothed particle hydrodynamics (SPH) is used to simulate hydrodynamic waves and wave phenomena including focusing from wave interference. This Lagrangian based method can be used to naturally simulate hydrodynamic free surfaces, including the free surface of a breaking wave. A virtual wave tank is simulated where wave motions can be excited from either side. Wave focusing is observed at the tank center, where the waves interfere. As a measure of the interference, the wave heights that result from focusing are presented. Certain types of wave focusing are thought to lead to large ocean waves. The efficacy of SPH in modeling wave focusing is critical to further understanding and predicting extreme wave phenomena with SPH.