The problem of water wave generation and attenuation by wind is proposed by numerically calculating the turbulent air flow over a third-order Stokes wave train. Most existing works [10, 28] have used a turbulent flow closure model of one equation type and assumed the flow to be aerodynamically rough to avoid the difficulties arising from the viscous sublayer. However, air flows over water waves are known to be aerodynamically transitional [26]. Thus, in this investigation we have adopted Sajjadi’s [24] roughness parameter to circumvent this difficulty. The turbulence model adopted for this investigation is based on the two equation closer scheme proposed by Saffman and Wilcox [21], and is used to simulate turbulent flow within and outside the viscous sublayer over steep non-linear surface waves. Thus, the present contribution is an extension to the earlier investigation of Al-Zanaidi and Hui [1]. The linearized turbulent flow equations for small (yet finite) wave slope are solved numerically up, and including, the third-order in wave steepness, taking into account the dynamical and kinematical boundary conditions at wave free surface. The resulting partial differential equations are first decomposed into a system of first order non-linear ordinary differential equations and solved numerically using the multiple shooting method [2]. The main aim of the present investigation is to calculate the vertical structure of wind field, the perturbation pressure as well as the fractional rate of energy input from wind to non-linear surface waves and hence calculate the energy transfer as well as the growth rate to a third-order Stokes wave due to turbulent shear flow flowing over it. The results show good agreement with computations of Conte and Miles [8] and also support the recent theoretical investigation of Sajjadi [24] for very high-Reynolds number (almost inviscid flow). The formation of Kelvin cat’s-eyes over a third-order Stokes waves is also calculated and their variations with the wave age show remarkable similarity with the work of Sullivan et al. [27].

air-sea interactions, turbulence model, third-order stokes waves.