Key Points: In the Navier-Stokes equations, a current is decomposed into four constituents, what allows separating the background and wave-induced Reynolds stresses. The explicit form of the wave-induced mixing function is found by the Reynolds-stress closure with using the turbulent viscosity in the wave-zone of the interface. The mixing function is linear in wave amplitude, resulting in enhanced impact of waves on a vertical mixing and related global geophysical processes.
AbstractIn 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, R w , from the background one, R b . To close R w , the Prandtl approach for the wave-induced fluctuations is used, resulting in the implicit expression for the wave-induced vertical mixing function, B v . Expression for B v is specified, basing on the author's 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 v (a, u * , z) is linear in both wave amplitude a(z) at depth z and friction velocity u * in the air. Due to depth-dependence a(z)~exp(kz), the found result for B v (a) means the possibility of the enhanced impact of waves on the vertical mixing and related geophysical processes, compared with the known cubic wave-amplitude dependence B v (a).