Hasselmann and coauthors proposed the discrete interaction approximation (DIA) as the best tool replacing the nonlinear evolution term in a numerical wind-wave model. Much later, Polnikov and Farina radically improved the original DIA by means of location all the interacting four wave vectors, used in the DIA configuration, exactly at the nodes of the numerical frequency-angular grid. This provides nearly two-times enhancing the speed of numerical calculation for the nonlinear evolution term in a wind-wave model. For this reason, the proposed version of the DIA was called as the fast DIA (FDIA). In this paper we demonstrate all details of the FDIA concept for several frequency-angular numerical grids of high resolution, with the aim of active implementation the FDIA in modern versions of world-wide used wind-wave models.

The aim of work is to derive an explicit expression for a function of vertical mixing induced by wind-waves. To this end, in the Navier-Stokes equations, a current is decomposed into four constituents: the mean flow, the wave-orbital motion, the wave-induced turbulent and the background turbulent currents. This decomposition allows separating the wave-induced Reynolds stress, Rw, from the background one, Rb. To make a statistical closure for Rw, the Prandtl approach for the background turbulent fluctuations is used that results in an implicit expression for the wave-induced vertical mixing function, Bv. Expression for Bv is specified based on the author’s results for the eddy viscosity found earlier in the frame of the three-layer concept for a wavy air–sea interface, used for modelling wind-drift currents [1]. Finally, the explicit parameterization for Bv(a, u*, z) is found as a linear function in both the wave amplitude at depth z, a(z), and the friction velocity in the air, u*. The linear dependence of function Bv(a) on the wave amplitude provides the enhanced vertical mixing induced by wind–waves in comparison with function Bv(a) having the cubic dependence found in [2], as far as the wind-wave amplitude a(z) decays exponentially with depth.