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

Open Journal of Marine Science 2014年第1期4卷 18-24页

作者： Augustin Daika theodule nkoa nkomom Cesar Mbane Biouele Laboratory of Earth’s Atmosphere Physics Department of Physics Faculty of Science University of Yaoundé I Yaoundé Cameroon

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 formulation 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.

关键词： Wind Stress Granular Targets Low Surface Tension Stationary Phase Method Stationary Gaussian

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Numerical Simulation of Water Waves’ Modulational Instability under the Effects of Wind’s Stress and Gravity Force Relaxation

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Open Journal of Marine Science 2016年第1期6卷 93-102页

作者： Théodule nkoa nkomom César Mbane Biouele Jeannot Mane Mane Laboratory of Earth’s Atmosphere Physics Department of Physics University of Yaoundé I Yaoundé Cameroun Ecole Nationale Supérieure Polytechnique (National Advanced School of Engineering) Department of Mathematics and Physical Sciences University of Yaoundé I Yaoundé Cameroon

The waves driven by the wind do not move on the water as ordinarily done by sailboats. Indeed, the movement of the waves driven by the wind is more complex than the sailboats’ translation movement that we know. The movement of the wave in our particular case results from the chain-job done by wind’s stress and gravity forces: material is collected upstream (erosion phenomenon) and then deposited on the wave’s summit by the wind. This material deposited on the summit of the wave by the wind is then removed and dispatched on the downstream side of the wave by gravity forces. As always happens in any chain-job: if the wind works faster than gravity forces, great accumulation of material will occur at the summit of the wave that will lead to an increase in its (the wave in this case) height. If conversely the wind works more slowly, a deficit in material delivery will occur and gravity force goes directly to remove material on the wave’s summit and lead to a decrease in its height. In terms of Mechanics, we know that the main obstacle that can seriously disturb the work of the wind is the unavailability of water or so its viscosity. Given the complexity of the process to be studied, it seemed necessary for us to make a use of modulational instability theories such as the standard NLSE in order to better understand the contribution of wind and water viscosity to modulations of driven waves’ amplitudes (or phases): modulations which sometimes can accidentally trigger unpredictable rogue waves.

关键词： Waves Driven by the Wind Standard Nonlinear Schrödinger Equation Modulations of Driven Waves’ Amplitudes or Phases Unpredictable Rogue Waves

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