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Wave shape (i.e. skewness or asymmetry) plays an important role in beachmorphology evolution, remote sensing, and ship safety. Wind's influence onocean waves has been extensively studied theoretically in the context ofgrowth, but most theories are phase averaged and cannot predict wave shape.Most laboratory and numerical studies similarly focus on wave growth. A fewlaboratory experiments have demonstrated that wind can change wave shape, andtwo-phase numerical simulations have also noted wind-induced wave shapechanges. However, wind's effect on wave shape is poorly understood, and notheory for it exists. For weakly nonlinear waves, wave shape parameters are thephase of the harmonic relative to the primary frequency (or harmonic phase HP,zero for a Stokes wave) and relative amplitude of the harmonic to the primary.Here, surface pressure profiles (denoted Jeffreys, Miles, and GeneralizedMiles) are prescribed based on wind-wave generation theories. Theoreticalsolutions are derived for quasi-periodic progressive waves and the wind-inducedchanges to HP, relative harmonic amplitude, as well as already known phasespeed changes and growth rates. The wave shape parameters depend upon thechosen surface pressure profile, pressure magnitude and phase relative to thewave profile, and the nondimensional depth. Wave asymmetry is linked to thenondimensional growth rate. Atmospheric large eddy simulations constrainpressure profile parameters. HP predictions are qualitatively consistent withlaboratory observations. This theory, together with the observables of HP andrelative harmonic amplitude, can provide insight into the actual wave surfacepressure profile.

Wind-Induced Changes to Surface Gravity Wave Shape in Deep to Intermediate Water