Experiments on nonlinear extreme waves in complex configurations

Abstract

Nonlinear rogue or freak waves are rare but utmost events in the ocean with at least twice the neighbouring wave heights. Understanding the properties of these events is crucial for ocean industry safety and expanding knowledge of the nonlinear hydrodynamic wave process. In addition to the dispersive focusing, i.e. the superposition of linear or nonlinear waves, it has recently been shown that both nonlinear focusing mechanisms play an important role in the description of rogue wave formation. In fact, the modulation instability (MI) is known to be active for the dimensionless depth value kh > 1.363, whereas the nonlinear wave shoaling takes place below this threshold value, and waves still being dispersive. The universal modulation instability (MI) is also responsible for the formation of strong wave localizations in other nonlinear media, such as optical Kerr media, plasma, and Bose- Einstein condensate. These wave-focusing dynamics can be described by breather solutions of the nonlinear Schrödinger equation (NLSE), such as the time-periodic Akhmediev breather(AB), space-periodic Kuznetsov-Ma breather (KB), and the space and time doubly-localized Peregrine breather (PB), which can seemingly "appear from nowhere and disappear without a trace". While the classical exact solutions of the NLSE have been extensively studied theoretically and experimentally, the integrability of the NLSE framework normally restricts them to the one-dimensional level and exact envelope shapes. Thus, the NLSE solutions differ from ordinary sea states, where wave shapes and directions are more arbitrary. In the current thesis, the role of wave nonlinearity in extreme wave formation beyond the analytical NLSE framework, i.e. under more complex wave configurations, was mainly investigated in two aspects: the effect of phase-shift and one particular case of wave field multi-directionality...(see the downloadable file for more)