Preprint Article Version 1 This version is not peer-reviewed

A Meso-Scale Approach to Estimating Vertical Mixing Induced by Wind–Waves

Version 1 : Received: 16 June 2019 / Approved: 18 June 2019 / Online: 18 June 2019 (05:44:29 CEST)

How to cite: Polnikov, V. A Meso-Scale Approach to Estimating Vertical Mixing Induced by Wind–Waves. Preprints 2019, 2019060167 (doi: 10.20944/preprints201906.0167.v1). Polnikov, V. A Meso-Scale Approach to Estimating Vertical Mixing Induced by Wind–Waves. Preprints 2019, 2019060167 (doi: 10.20944/preprints201906.0167.v1).

Abstract

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.

Subject Areas

air-sea interface; wind–waves; turbulent currents; Reynolds stress; vertical mixing; eddy viscosity

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