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Ayoub MANSAR
Numerical study of the Breaking of Short-Crested Waves : Breaking Onset, Energy Dissipation and Superharmonic Instability
Abstract
Wave breaking plays a crucial role in energy dissipation and turbulent mixing at the ocean surface. Accurate predictions require robust breaking criteria and dissipation models. While most studies focus on two-dimensional systems, this thesis incorporates three-dimensional effects into wave breaking dynamics. The first part investigates 3D short-crested wave breaking through Direct Numerical Simulation (DNS), using the parameter θ to represent the degree of three-dimensionality. Both progressive waves (θ = 90°) and fully 3D cases (θ < 90°) are analyzed. Geometrical and kinematic breaking criteria, including the universal kinematic/dynamic criterion, are assessed. The 2D limiting slope (1/tan(60°) ≈ 0,5774) accurately distinguishes breaking from non-breaking for (θ ≥ 45°), while kinematic criteria fail near the standing wave limit. Energy dissipation scaling with steepness holds up to (θ = 63°), and the steepness dependency is reduced for (θ ≤ 45°).
The second part examines the superharmonic (SH) instability as a potential cause for 3D wave breaking in deep water. We explore SH instability's role in localized breaking, motivated by the connection between observed 3D dynamics and linear stability analysis. DNS simulations for (θ = 63°) reveal crescent-shaped patterns near the crest that evolve into localized breaking. The instability from these simulations aligns with SH eigenfunctions. To validate this, a 2D DNS campaign used an SVD-based filtering algorithm to extract unstable modes, showing a dipole structure consistent with SH instability.
Keywords
- short-crested waves,
- wave breaking criteria,
- energy dissipation,
- superharmonic instability
Supervision
Jury
- Emmanuel DORMY, Directeur de recherche, ENS Ulm, Rapporteur
- Iraj MORTAZAVI, Professeur des universités, CNAM, Rapporteur
- François ALOUGES, Professeur des universités, ENS Paris-Saclay, Examinateur
- Laure QUIVY, Maîtresse de conférences, ENS Paris-Saclay, Examinatrice
- John GRUE, Professor, University of Oslo, Examinateur