The influence of wind on extreme wave events in deep water is investigated experimentally and numerically. A series of experiments conducted in the Large Air–Sea Interactions Facility (LASIF-Marseille, France) shows that wind blowing over a short wave group due to the dispersive focusing of a longer frequency-modulated wavetrain (chirped wave packet) may increase the time duration of the extreme wave event by delaying the defocusing stage. A detailed analysis of the experimental results suggests that extreme wave events may be sustained longer by the air flow separation occurring on the leeward side of the steep crests. Furthermore it is found that the frequency downshifting observed during the formation of the extreme wave event is more important when the wind velocity is larger. These experiments have pointed out that the transfer of momentum and energy is strongly increased during extreme wave events.Two series of numerical simulations have been performed using a pressure distribution over the steep crests given by the Jeffreys sheltering theory. The first series corresponding to the dispersive focusing confirms the experimental results. The second series which corresponds to extreme wave events due to modulational instability, shows that wind sustains steep waves which then evolve into breaking waves. Furthermore, it was shown numerically that during extreme wave events the wind-driven current could play a significant role in their persistence.

The modulational instability of gravity wave trains on the surface of water acted upon by wind and under influence of viscosity is considered. The wind regime is that of validity of Miles' theory and the viscosity is small. By using a perturbed nonlinear Schrödinger equation describing the evolution of a narrow-banded wavepacket under the action of wind and dissipation, the modulational instability of the wave group is shown to depend on both the frequency (or wavenumber) of the carrier wave and the strength of the friction velocity (or the wind speed). For fixed values of the water-surface roughness, the marginal curves separating stable states from unstable states are given. It is found in the low-frequency regime that stronger wind velocities are needed to sustain the modulational instability than for high-frequency water waves. In other words, the critical frequency decreases as the carrier wave age increases. Furthermore, it is shown for a given carrier frequency that a larger friction velocity is needed to sustain modulational instability when the roughness length is increased.

A nonlinear Schrödinger equation for the envelope of two-dimensional gravity–capillary waves propagating at the free surface of a vertically sheared current of constant vorticity is derived. In this paper we extend to gravity–capillary wave trains the results of Thomas et al. (Phys. Fluids, 2012, 127102) and complete the stability analysis and stability diagram of Djordjevic & Redekopp (J. Fluid Mech., vol. 79, 1977, pp. 703–714) in the presence of vorticity. The vorticity effect on the modulational instability of weakly nonlinear gravity–capillary wave packets is investigated. It is shown that the vorticity modifies significantly the modulational instability of gravity–capillary wave trains, namely the growth rate and instability bandwidth. It is found that the rate of growth of modulational instability of short gravity waves influenced by surface tension behaves like pure gravity waves: (i) in infinite depth, the growth rate is reduced in the presence of positive vorticity and amplified in the presence of negative vorticity; (ii) in finite depth, it is reduced when the vorticity is positive and amplified and finally reduced when the vorticity is negative. The combined effect of vorticity and surface tension is to increase the rate of growth of modulational instability of short gravity waves influenced by surface tension, namely when the vorticity is negative. The rate of growth of modulational instability of capillary waves is amplified by negative vorticity and attenuated by positive vorticity. Stability diagrams are plotted and it is shown that they are significantly modified by the introduction of the vorticity.

A numerical investigation of normal-mode perturbations of a two-dimensional periodic finite-amplitude gravity wave propagating on a vertically sheared current of constant vorticity is considered. For this purpose, an extension of the method developed by Rienecker & Fenton (J. Fluid Mech., vol. 104, 1981, pp. 119–137) is used for the numerical computations of the finite-amplitude waves on a linear shear current. This method enables to compute accurately waves with or without critical layers and pressure anomalies. The numerical results of the linear stability analysis extend the weakly nonlinear analytical results of Thomas et al. (Phys. Fluids, vol. 24, 2012, 127102) to fully nonlinear waves. In particular, the restabilization of the Benjamin–Feir modulational instability, whatever the depth, for an opposite shear current is confirmed. For these sideband instabilities, the numerical results show some deviations with the weakly nonlinear theory as the wave steepness of the basic wave and vorticity are increased. Besides the modulational instabilities, new instability bands corresponding to quartet and quintet instabilities, which are not sideband disturbances, are discovered. The present numerical results show that with opposite shear currents, increasing the shear reduces the growth rate of the most unstable sideband instabilities but enhances the growth rate of these quartet instabilities, which eventually dominate the Benjamin–Feir modulational instabilities.