Descriptions of unusually high waves appearing on the sea surface for a short time (freak, rogue or killer waves) have been considered as a part of marine folklore for a long time. A number of instrumental registrations have appeared recently making the community to pay more attention to this problem and to reconsider known observations of freak waves. To allow a better understanding of the behavior of rogue waves associated with tornadoes in terms of their origin, the nonlinear theory of off-balance systems is developed in the specific case of strong agitations constantly seen on the surface of extensive and deep rivers, when they are crossed by an atmosphere's low pressure system (tornadoes, cyclones, hurricanes, etc.). A mathematical model based on the Navier-Stokes and Euler Lagrange equations coupled with assumptions derived from instrumental registrations on the training locations (or birth places) of freak waves is developed to enhance the physics of processes responsible for the formation (or origin) of the waves associated with atmosphere's low pressure systems. Freak waves births' constraints are mainly the need for both consistent water (i.e., extensive-deep rivers) and potential velocity flow availabilities. Numerical simulations, based on the use of the NLSE (Nonlinear Schrödinger Equation) are performed to validate our mathematical model on the births of single carrier waves associated with atmosphere's low pressure systems.
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.
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