Sheared turbulence in a weakly stratified upper ocean

Microstructure, ADCP and CTD profiles taken in the North Atlantic along 53 degrees N under moderate and high winds showed that the median of log-normally distributed kinetic energy dissipation rate e within the upper mixing layer is 1.5 x 10(-7) W/kg and the layer depth, on the average, is similar to 40 m. Assuming that mixing efficiency gamma is a constant (gamma = 0.2), the following scaling is proposed for the normalized eddy diffusivity: K-b = K-b/ ku(*)z = (1 + Ri/Ri(cr))(-p) Pr-tr(-1), where K-b = gamma e/N-2, N-2 is the squared buoyancy frequency, u(*) the surface friction velocity, Ri the local Richardson number, Pr-tr = 1 + Ri/Ri(beta) the turbulent Prandtl number, p = 1 or 2/3, Ri(cr) = 0.1 and Ri(beta) = 0.1 or 0.05. The power-law function with p = 1 relates the asymptotes of K-b(Ri) to the buoyancy scale L-N similar to (epsilon/N-3)(1/2) at Ri >> Ri(cr) and to the shear scale L-Sh similar to(epsilon/Sh(3))(1/2) at Ri << R-ir. If p = 2/3, the lengthscale L-R = (epsilon/N(2)Sh)(1/2) replaces L-N in spectra of ocean microstructure than due to the influence of local shear. This mixing regime corresponds to intermediate Richardson numbers (similar to 0.25 < Ri < similar to 2). Alternatively, if gamma 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 R-i < 0.25. Numerical experiments using a one-dimensional q(2)-epsilon model with different K-b parameterizations indicate that the measured mixed-layer depth agrees well with model results when the diffusivity is parameterized with an Ri-dependent gamma (the GISS model approach). The modeled dissipation profiles, however, resembled microstructure measurements better if gamma is treated as a constant and the proposed formula for K-b(Ri) is used. (c) 2005 Elsevier Ltd. All rights reserved.