A Model of the Enhanced Vertical Mixing Induced by Wind-Waves

TL;DR

This paper develops an explicit model for wave-induced vertical mixing in the ocean, showing how waves can significantly enhance mixing compared to previous cubic dependence models, with implications for geophysical processes.

Contribution

It introduces a new explicit expression for the wave-induced vertical mixing function based on turbulent viscosity and wave amplitude, improving understanding of wave effects on mixing.

Findings

Enhanced vertical mixing due to wave amplitude

Linear dependence of mixing function on wave amplitude and friction velocity

Potential for stronger wave impact on geophysical processes

Abstract

In the Navier-Stokes equations, a current is decomposed into four constituents: the mean flow, wave-orbital motion, wave-induced-turbulent and background-turbulent currents. Under certain statistical assumptions, this allows to separate the wave-induced Reynolds stress from the background one. To close the wave-induced Reynolds stress, the Prandtl approach for the wave-induced fluctuations is used, resulting in the implicit expression for the wave-induced vertical mixing function, B. Expression for B is specified, basing on the author results for the turbulent viscosity, found earlier in the frame of the three-layer concept for the air-sea interface. The explicit expression for function B is linear in both wave amplitude and friction velocity in the air. Due to exponential decay of wave amplitude, the found result means the possibility of the enhanced impact of waves on the vertical mixing and related geophysical processes, compared to the known cubic wave-amplitude dependence for B, found by Qiao et al previously.