Biography
Biography: Anouchah Latifi
Abstract
In this work, we present the extension of the Miles’ and Jeffreys’ theories of the wind wave generation to finite depth through three different approaches; linear approach, quasi-linear approach and fully nonlinear approach. In the first case, the dispersion relation provides a depth dependent wave growth rate providing a good agreement with the data from the Australian shallow water experiment as well as the data from the Lake George experiment. In the second case, the evolution of wind waves in finite depth is reduced to an anti-dissipative Korteweg-de Vries-Burgers equation, and its solitary wave solution is exhibited presenting blow up and breaking in finite time. Finally, in the third case, the full nonlinear Green-Naghdi model equation is derived and two families of growth rate and their allowed minimum and maximum values are exhibited.