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.
Keywords:
Subject: Environmental and Earth Sciences - Oceanography
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
Preprints.org is a free preprint server supported by MDPI in Basel, Switzerland.