Observations and scaling of the upper mixed layer in the North Atlantic

[1] The dependence of the mixed layer depth h(D) on the sea surface fluxes is analyzed based on measurements taken along a cross-Atlantic section 53 degrees N. A linear function h(D) approximate to 0.44L(f), where L-f = u(*)/f is the Ekman scale, well represents the influence of the wind stress u(*) and rotation f on the mixed-layer deepening, thus indicating that the influence of convective mixing in late spring at this latitude is of a lesser importance. Also, data showed reasonable correlation of hD with the stratified Ekman scale L-fN = u(*)/root fN(pc) , where N-pc is the buoyancy frequency in the pycnocline, according to h(D) approximate to 1.9L(fN). In both cases the highest correlation between h(D) and the corresponding lengthscales is achieved when u* values taken 12 hours in advance of the mixed layer measurements were used, which may signify the adjustment time of inertial oscillations to produce critical shear at the base of the mixed layer. The vertical profiles of the dissipation rate epsilon(z) are parameterized by two formulae that are based on the law of the wall scaling epsilon(s)(z) = u(*) (3)/ 0.4z and the buoyancy flux J(b): epsilon(1)( z) = 2.6 epsilon(s)(z) + 0.6J(b) and epsilon(2)( z) = epsilon(s)(z) epsilon(s)( z) + 3.7J(b). The first parameterization is used to calculate the integrated dissipation (epsilon) over tilde (int) over the mixing layer, which was found to be similar to 3 - 7% (5% on the average) of the wind work E-10. The positive correlation between h(D) and (epsilon) over tilde (int)/E-10 suggests that in deeper quasi-homogeneous layers a larger portion of the wind work is consumed by viscous dissipation vis-a-vis that is used for entrainment. As such, the mixing efficiency, which is based on integral quantities, is expected to decrease with the growth of the mixed layer.