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 = 0.2 ), the following scaling is proposed for the normalized eddy diffusivity: K ^ b = K b / κ u * z = ( 1 + Ri / R i cr ) - p P r tr - 1 , where K b = γ ε / N 2 , N2 is the squared buoyancy frequency, u * the surface friction velocity, Ri the local Richardson number, P r tr = 1 + Ri / R i β the turbulent Prandtl number, p = 1 or 2/3, Ricr=0.1 and Riβ=0.1 or 0.05. The power-law function with p = 1 relates the asymptotes of Kb(Ri) to the buoyancy scale L N ∼ ( ε / N 3 ) 1 / 2 at Ri⪢Ricr and to the shear scale L Sh ∼ ( ε / Sh 3 ) 1 / 2 at Ri⪡Ricr. If p = 2 / 3 , the lengthscale L R = ( ε / N 2 Sh ) 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<Ri<∼2). atively, if γ is not a constant, but an increasing function of Ri for 0<Ri<1, then K ^ b ( Ri ) shows a very weak dependence on Ri for Ri<0.25. Numerical experiments using a one-dimensional q2−ε model with different Kb parameterizations indicate that the measured mixed-layer depth agrees well with model results when the diffusivity is parameterized with an Ri-dependent γ (the GISS model approach). The modeled dissipation profiles, however, resembled microstructure measurements better if γ is treated as a constant and the proposed formula for K ^ b ( Ri ) is used.