TITLE:
Numerical Simulation of Water Waves’ Modulational Instability under the Effects of Wind’s Stress and Gravity Force Relaxation
AUTHORS:
Théodule Nkoa Nkomom, César Mbane Biouele, Jeannot Mane Mane
KEYWORDS:
Waves Driven by the Wind, Standard Nonlinear Schrödinger Equation, Modulations of Driven Waves’ Amplitudes or Phases, Unpredictable Rogue Waves
JOURNAL NAME:
Open Journal of Marine Science,
Vol.6 No.1,
January
29,
2016
ABSTRACT: 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.