Wind-induced changes to surface gravity wave shape in deep to intermediate water

Wave shape (i.e. skewness or asymmetry) plays an important role in beach morphology evolution, remote sensing and ship safety. The wind's influence on ocean waves has been extensively studied theoretically in the context of growth, but most theories are phase averaged and cannot predict wave shape. Most laboratory and numerical studies similarly focus on wave growth. A few laboratory experiments have demonstrated that wind can change wave shape, and two-phase numerical simulations have also noted wind-induced wave-shape changes. However, the wind's effect on wave shape is poorly understood, and no theory for it exists. For weakly nonlinear waves, wave-shape parameters are the phase of the first harmonic relative to the primary frequency (or harmonic phase HP, zero for a Stokes wave) and relative amplitude of the first harmonic to the primary wave. Here, surface pressure profiles (denoted Jeffreys, Miles and generalized Miles) are prescribed based on wind–wave generation theories. Theoretical solutions are derived for quasi-periodic progressive waves and the wind-induced changes to the HP, relative harmonic amplitude, as well as the already known phase speed changes and growth rates. The wave-shape parameters depend upon the chosen surface pressure profile, pressure magnitude and phase relative to the wave profile and non-dimensional depth. Wave asymmetry is linked to the non-dimensional growth rate. Atmospheric large eddy simulations constrain pressure profile parameters. The HP predictions are qualitatively consistent with laboratory observations. This theory, together with the HP and relative harmonic amplitude observables, can provide insight into the actual wave surface pressure profile.