Extended nonlinear theory for water wave modulations under strong winds

The fourth-order weakly nonlinear theory for modulated wind waves has been derived for a nonlinear-generalized Miles' surface pressure term. The situation of unidirectional waves and a strong wind is considered. The focus is made on the conditions of great and intermediate water depths. Dynamic effects associated with the nonlinear character of the wind–wave interaction have been identified, such as the saturation or intensification of the wind–wave energy exchange, the alteration of the wave and wavegroup shapes including modification of the nonlinear induced flow when the depth is finite, and the complicated picture of the modulational instability. We suggest that a sudden change in wind intensity or direction may contribute to the occurrence of rogue waves due to the wind-dependent bound waves.