Simplified model of the air flow above waves

A simplified model of the air flow over surface water waves propagating at arbitrary phase velocity as compared to the wind velocity is presented. The approach is based on the subdivision of the air flow into an outer (OR) an d an inner (IR) region. In the OR the wave-induced motion experiences invis cid undulation, while in the IR it is strongly affected by the turbulent sh ear stress. The subdivision of the air flow into two regions considerably s implifies the solution of the problem. The critical height (the height wher e the wind speed and the wave phase velocity are equal) is for most cases l ocated inside the IR. Its singular behaviour is strongly suppressed by turb ulence. The description of the wind velocities in the OR is based on an app roximate solution of the Rayleigh equation. The description of the IR is ba sed on the solution of the vorticity equation accounting for turbulent diff usion. The local eddy-viscosity mixing length closure scheme is used to par ameterize the turbulent shear stress. Exponential damping of the shear stre ss variation with height towards the OR is introduced. This damping describ es phenomenologically the basic feature of the wave boundary layer: a rapid distortion of turbulence in the OR. Wave-induced velocity and shear stress profiles, and the wave growth rate, resulting from the model show reasonab le agreement with those obtained by a two-dimensional numerical model based on a second-order closure scheme. Moreover, the velocity profiles are in g ood agreement with laboratory measurements.