Numerical simulation of freak wave events
Vincent Gigante2006
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Abstract
This report deals with extreme wave phenomena. Exploration of the classical wave theories are made, both on the theoratical approach and on the statistical one. The first one shows wave generation phenomenon using only Euler's equation for a perfect fluid and gravity. On the other one, the statistical approach provides us with more real observations. Both models fail to explain some rare (or not so rare ?) events: freak waves. Then we defined what is a freak wave and some of the explanations that are given. Exploration on the non linear Schrödinger equation, which is known to give birth to gigantic waves is then the path taken. This equation could be easily derived from Euler's equations. Numerical solution of this equation are provided in the last chapter. Finally, the third part deals with spectral methods and how they are used to compute very easily non linear interaction for waves. Last chapter provides also results on this. In fact, the last chapter is devoted to the results obtained, either on solving NLS, either on the computation of surface waves.
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