Application of Stationary Phase Method to Wind Stress and Breaking Impacts on Ocean Relatively High Waves

Abstract

Wind stress impacts on ocean relatively high waves can be perfectly illustrated by a recurrent phenomenon in the Sahara desert. Indeed, on this area where the surface wind can blow without encountering major obstacle out of the sand dunes, these main targets are gradually eroded and displaced by the wind on dozens of meters. This experience highlights the action of wind on granular targets (clusters of sand or water slides) and motivates studies similar to ours, where we want to simulate impact of wind stress and breaking on the spatio-temporal evolution of the envelope of ocean relatively high waves: Impact which can inappropriately deflect the waves on ships, oil platforms or coastal infrastructures. Euler and Navier-Stokes equations allow a mathematical formula tion of the gravity wave motion (ocean waves are considered in our work as a system of water particles which are held together by low surface tension) and wind acts on targets through friction forces or stress. Michel Talon stationary phase method is used to numerically solve the equations that model the impact of wind on a stationary Gaussian.