Two-dimensional direct numerical simulations of the dynamics of rogue waves under wind action
Résumé
The understanding of the role of water waves in air-sea interaction is of prime importance to improve approximate wave models predicting the sea state, namely the action balance equation which is forced by wind input, wave-wave interactions and dissipation. In this equation the physics is embodied in a set of source functions whose modelling can be improved through a more detailed analysis based on the numerical simulation of the fully nonlinear equations of water waves. The knowl- edge of velocity, acceleration and pressure ¯elds of extreme wave events such as rogue waves is crucial for computing loads on structures, ship routing and human safety. The dynamics of these huge waves which are strongly nonlinear phenomena can be properly determined only by integrating numerically the fully nonlinear governing equations. Two numerical methods are presented and used to study the dynamics of rogue waves in the presence of wind: A High-Order Spectral Method (HOSM) and a Boundary Integral Equation Method (BIEM). For both numerical methods the convergence and accuracy of the models are tested using exact solutions or experimental data.