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Wave-seabed interaction and mechanisms of freak wave formation in coastal zones

Abstract : In the maritime community, the term "rogue wave" or “freak wave” is used for waves whose wave height exceeds twice the significant wave height of the ambient sea state, and which appear more frequently than predicted by the Rayleigh distribution for wave height based on a Gaussian sea state hypothesis. In the oceanic domain, rogue waves that have caused loss of lives and severe damage have been widely reported in recent decades. In coastal areas, irregular bathymetry can also trigger such high extreme waves due to seabed-wave interactions. In this thesis, we focus on three mechanisms or scenarios of wave-bottom interactions that can lead to the formation of high waves.The first scenario is a resonance phenomenon, known as Fabry-Perot resonance, which can develop when monochromatic waves propagate over a bathymetry with two areas of sinusoidal undulations on an otherwise flat bottom. In the resonator zone located between the two areas of ripples, a significant increase in the height of the incident wave can be obtained if the resonance condition is met. By comparing numerical simulations with either exact or approximated bottom boundary condition and an asymptotic linear analytical solution, we observe a shift of the resonance frequency at the resonance condition for cases where the ratio between the amplitude of the ripples and the water depth is large: resonance occurs for a smaller wave number than predicted by the approximate analytical theory. This downshift effect of resonance frequency plays a secondary role for Bragg resonance, but it is very important and sensitive for Fabry-Perot resonance.The second scenario corresponds to the instabilities of amplitude modulated wave trains, commonly called "breathers", which propagate over irregular bottoms. Three types of bathymetric profiles are studied experimentally and numerically with a fully nonlinear model and with nonlinear (cubic) Schrödinger equation. This study has shown that for shallow depths and for certain conditions, the amplitude of the modulation can reach twice the amplitude of the initial train. This shallow depth amplification results from mechanisms that do not exist at constant depth. The influences of parameters that can affect the dynamics of breathers, including the Akhmediev breather parameter, water depth, steepness of the carrier wave, wave period and bottom slopes are analysed.The third scenario corresponds to unidirectional irregular wave trains propagating on variable coastal bottom profiles. When an incident sea state in equilibrium condition passes over a submerged bar or step, non-equilibrium dynamics appear and force the sea state to a new equilibrium compatible with the finite depth, characterized by highly non-Gaussian statistics and an increased probability of extreme wave occurrence. The combination of large-scale experiments and fully nonlinear simulations allows a better understanding of the dynamic response of the wave train. The resulting data were analysed in depth using a combination of spectral, bispectral and statistical approaches.
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Jie Zhang. Wave-seabed interaction and mechanisms of freak wave formation in coastal zones. Fluids mechanics [physics.class-ph]. Ecole Centrale Marseille, 2020. English. ⟨NNT : 2020ECDM0003⟩. ⟨tel-03120496⟩

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