The influence of stratification, and by inference viscosity, on the shears can be isolated by considering the diurnal cycle since the wind and front have little diurnal variability. Figure 5 shows the diurnal composite of the wind, near-surface currents relative to 25 m, and temperature, computed over the 4.5-month period when all five current meters were functioning. The top 25 m is isothermal (or even slightly unstable) at nighttime and is weakly stratified during the afternoon. Because the diurnal cycle of the winds is very weak, diurnal variations in the shear must be due to the influence of mixing and stratification (Price et al. 1986; Lien et al. 1995): During the afternoon, the albeit weak [0.1°C (10 m)−1] stratification causes the wind-generated momentum to be trapped within the shallow mixed layer. The shear associated with the afternoon "diurnal" jet is roughly aligned with the wind, while below the jet the shear is more zonal. By 1600 local time, the diurnal jet has currents at 5 m that are more than 12 cm s−1 stronger than at 25 m. As the diurnal warm layer cools and thickens during the late afternoon–early evening, the anomalous wind current can be seen at ever greater depths.
Fig. 5. Mean diurnal composite (24 May 2004–7 Oct 2004) of wind (blue vectors), temperature (color shading), and currents relative to 25 m (black vectors). The vector scale is shown at the bottom.
To better understand the mixing physics and viscosity properties associated with the diurnal cycle, a composite Richardson number is computed by dividing the composite buoyancy frequency (N2 = −g/ρ0 ∂ρ/∂z) by the composite squared shear (i.e., Ri = N2/|∂u/∂z|2). This method was found to be less noisy than computing the composite directly from the 20-min Ri time series. It should be noted that most Ri-based parameterizations of viscosity are not valid for unstable stratification in which Ri is negative. For example, in the commonly used Pacanowski and Philander (1981) parameterization, viscosity has a maximum value of 10.1 × 10−3 m2 s−1 for Ri = 0, while in the Peters et al. (1988) parameterization viscosity becomes unbound as Ri approaches zero. Since, Ri is slightly negative during nighttime (Fig. 6), indicating active convective mixing, nighttime turbulent viscosity is likely significantly larger than 10 × 10−3 m2 s−1. In contrast, between 1200 and 1400 local time, daytime warming causes stratification near 10 m to increase. The resulting Ri is larger than 0.25 and viscosity is thus expected to be smaller [roughly 2 × 10−3 m2 s−1 according to the Pacanowski and Philander (1981) and Peters et al. (1988) formulations]. At all other depths and times, Ri is less than 0.25, but positive, indicating that shear instability mixing is likely occurring. Interestingly, the critical Ri value of 0.25 appears to propagate downward with time, suggesting that as mixing transmits the wind-generated momentum and solar radiation warmed water to greater depths, shear is introduced, which causes the mixing to also be transmitted to greater depths, consistent with the model study of Danabasoglu et al. (2006). Averaged over the full diurnal cycle, the observed mean Ri increases with depth (Fig. 7), indicating that viscosity decays with depth, consistent with the assumption in our generalized Ekman model (7).
Fig. 6. Mean diurnal composite of (a) buoyancy frequency N2, (b) shear squared, and (c) Richardson number. The units in (a) and (b) are 10−4 s−1; Ri in (c) is nondimensional.
Fig. 7. Mean profiles of N2 (short dashed), shear squared (long dashed), and Ri (solid) averaged over the diurnal composite shown in Fig. 6.
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