École Nationale Supérieure de
Techniques Avancées

Résumé

This research investigates the dynamics of focused and rogue waves in fluid mechanics through mathematical modeling, experimental validation, and numerical simulation. The study begins by exploring the Modified Nonlinear Schrödinger Equations (MNSE), including the Peregrine Soliton, modulated instabilities, Akhmediev breathers, and the Dysthe equation, crucial for understanding wave evolution. Experimental work compares breaking models in wave evolution equations using laboratory and wave tank experiments, examining the link between focused waves and rogue waves. Advanced data processing techniques refine model comparisons and improvements. In the numerical simulation, the research outlines methods to approach solutions, emphasizing the relationship between bandwidth and full width at half maximum (FWHM). Stabilization methods, including adaptive time stepping, enhance simulation accuracy. The study also explores wind-induced rogue wave formation. The findings, supported by case-specific studies, advance the understanding of focused wave phenomena and contribute to the development of more accurate predictive models in fluid mechanics.