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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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