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The original investigation of Lamb (1932, {\S}349) for the effect ofviscosity on monochromatic surface waves is extended to account forsecond-order Stokes surface waves on deep water in the presence of surfacetension. This extension is used to evaluate interfacial impedance for Stokeswaves under the assumption that the waves are growing and hence the surfacewaves are unsteady. Thus, the previous investigation of Sajjadi et al. (2014)is further explored in that (i) the surface wave is unsteady and nonlinear, and(ii) the effect of the water viscosity, which affects surface stresses, istaken into account. The determination of energy-transfer parameter, from windto waves, are calculated through a turbulence closure model but it is shown thecontribution due to turbulent shear flow is some 20% lower than that obtainedpreviously. A derivation leading to an expression for the closed streamlines(Kelvin cat-eyes), which arise in the vicinity of the critical height, is foundfor unsteady surface waves. From this expression it is deduced that as wavesgrow or decay, the cats-eye are no longer symmetrical. Also investigated is theenergy transfer from wind to short Stokes waves through the viscous Reynoldsstresses in the immediate neighborhood of the water surface. It is shown thatthe resonance between the Tollmien-Schlichting waves for a given turbulent windvelocity profile and the free-surface Stokes waves give rise to an additionalcontribution to the growth of nonlinear surface waves.

Growth of Stokes Waves Induced by Wind on a Viscous Liquid of Infinite Depth