Ekman Layer Rectification

Abstract

Abstract The phenomenon of oceanic Ekman layer rectification refers to how the time-mean, Ekman layer velocity profile with depth differs as a consequence of variability in the surface wind in addition to the time-mean wind. This study investigates rectification using the K-Profile Parameterization (KPP) model for the turbulent surface boundary layer under simple conditions of uniform density and no surface buoyancy flux or surface wave influences. The rectification magnitude is found to be significant under typical conditions. Its primary effects are to extend the depth profile deeper into the interior, reduce the mean shear, increase the effective eddy viscosity due to turbulent momentum mixing, and rotate slightly the surface velocity farther away from the mean wind direction. These effects are partly due to the increase in mean stress because of its quadratic dependence on wind speed but also are due to the nonlinearity of the turbulent mixing efficiency. The strongest influence on the rectification magnitude is the ratio of transient wind amplitude to mean wind speed. It is found that an accurate estimate of the mean current usually can be obtained by using a quasi-stationary approximation that is a weighted integral of the steady Ekman layer response over the probability density function for the wind, independent of the detailed wind history. Rectification occurs even for very high frequency wind fluctuations, though the accuracy of the quasi-steady approximation degrades in this limit (as does the validity of the KPP model). This theory is extended to include the effects of the horizontal component of the Coriolis frequency, f y. Based on published computational turbulence solutions, a simple parameterization is proposed that amplifies the turbulent eddy diffusivity in KPP by a factor that decreases with latitude and depends on the wind orientation. The effect of f y ≠ 0 is to increase both the shear and the surface speed in the time-mean Ekman current for winds directed to the northeast and decrease both quantities for winds to the southwest, with weaker influences on these properties for the orthogonal directions of southeast and northwest. Furthermore, with transient winds there is significant coupling between f y ≠ 0 and the rectification effect; for example, the mean surface current direction, relative to the mean wind, is significantly changed for these orthogonal directions.