Sheared turbulence in a weakly stratified upper ocean

Microstructure, ADCP and CTD profiles taken in the North Atlantic along 53°N under moderate and high winds showed that the median of log-normally distributed kinetic energy dissipation rate ε within the upper mixing layer is 1.5×10−7 W/kg and the layer depth, on the average, is ∼40 m. Assuming that mixing efficiency γ   is a constant (γ=0.2γ=0.2), the following scaling is proposed for the normalized eddy diffusivity:K^b=Kb/κu*z=(1+Ri/Ricr)-pPrtr-1,where Kb=γε/N2Kb=γε/N2, N2 is the squared buoyancy frequency, u*u* the surface friction velocity, Ri   the local Richardson number, Prtr=1+Ri/RiβPrtr=1+Ri/Riβ the turbulent Prandtl number, p=1p=1 or 2/3, Ricr=0.1 and Riβ  =0.1 or 0.05. The power-law function with p=1p=1 relates the asymptotes of Kb(Ri  ) to the buoyancy scale LN∼(ε/N3)1/2LN∼(ε/N3)1/2 at Ri⪢Ricr and to the shear scale LSh∼(ε/Sh3)1/2LSh∼(ε/Sh3)1/2 at Ri⪡Ricr. If p=2/3p=2/3, the lengthscale LR=(ε/N2Sh)1/2LR=(ε/N2Sh)1/2 replaces LN in spectra of ocean microstructure than due to the influence of local shear. This mixing regime corresponds to intermediate Richardson numbers (∼0.25