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

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.