The original investigation of Lamb [3, Section 349] for the effect of viscosity on monochromatic surface waves is extended to account for second-order Stokes surface waves on deep water in the presence of surface tension. This extension is used to evaluate interfacial impedance for Stokes waves under the assumption that the waves are growing and hence the surface waves are unsteady. Thus, the previous investigation of Sajjadi et al. [14] 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, is taken into account. The determination of energy-transfer parameter, from wind to waves, is calculated through a turbulence closure model but it is shown the contribution due to turbulent shear flow is some 20% lower than that obtained previously. A derivation leading to an expression for the closed streamlines (Kelvin cat-eyes), which arise in the vicinity of the critical height, is found for unsteady surface waves. From this expression, it is deduced that as waves grow or decay, the cats-eye is no longer symmetrical. Besides, the energy transfer from wind to short Stokes waves through the viscous Reynolds stresses in the immediate neighborhood of the water surface is investigated. It is shown that the resonance between the Tollmien-Schlichting waves for a given turbulent wind velocity profile and the free-surface Stokes waves give rise to an additional contribution to the growth of nonlinear surface waves.

air-sea interactions, Stokes wave, water waves.