Advection-diffusion models of the oceanic thermocline require a global ocean, mean vertical eddy diffusivity of about 1 cm2 s-1; however, maximum values estimated from microstructure measurements at mid-gyre locations are generally smaller and, occasionally, 1-2 orders of magnitude less, depending on the particular assumptions made by individual analysts. Mesoscale features are high kinetic energy sources, which may fuel vertical mixing mechanisms on fine structure scales, resulting in local enhancements of eddy diffusivity above the canonical value of 1 cm2 s-1. The effects of one such mechanism, the Kelvin-Helmholtz instability, are assessed for a Gulf Stream ring and a mid-thermocline eddy. The necessary Richardson numbers are computed from Yvette profiles obtained in these features and are accurate to within about 10% for Ri=1, and more accurate at the critical value Ri=0.25. A plausible extension of the Miles-Howard theorem for a nonparallel shear flow is formulated for a two-dimensional perturbation. The shear appropriate for this Richardson number calculation is well approximated by the total shear for slowly depth-varying direction, as is the case fr the vast majority of the data. Upper and lower bounds on the vertical scale for the Richardson number calculation are set by the shear spectra and the Ozmidov scale. Median Richardson number was lower toward the center of the eddy because of a large decrease in Brunt-Vaisala frequency (N2) and was depressed on the fringes by high shear. Lower median Ri is also found at the center of the ring as a result of low N2. Lower bounds on vertical eddy diffusivity are estimated based on the assumptions of a simple, mixing-length model and of complete mixing of each region where Ri is less than 0.25. The spatial distribution of this quantity within the eddy and the ring mirrors that of median Ri. Values range from Az ~1.1 cm2 s-1 near the center of the eddy and 0.90 cm2 s-1 near the center of the ring to zero in regions outside of the features where no Ri less than 0.25 were observed.