On the interaction of wind and steep gravity wave groups using Miles’ and Jeffreys’ mechanisms

The interaction of wind and water wave groups is investigated theoretically and numerically. A steep wave train is generated by means of dispersive focusing, using both the linear theory and fully nonlinear equations. The linear theory is based on the Schrödinger equation while the nonlinear approach is developed numerically within the framework of the potential theory. The interaction between the chirped wave packet and wind is described by the Miles’ mechanism. The differences between both approaches are discussed, and the influence of nonlinearity is emphasized. Furthermore, a different mechanism is considered, described by the modified Jeffreys’ sheltering theory. From comparison between the two mechanisms, it is found that the persistence of the steep wave group depends on the physical model used, and is significantly increased when we use the latter mechanism.