Ocean models require subgrid-scale parametrizations of vertical mixing expressed in terms of a quantity that is easily diagnosable from model output, such as the Richardson number. To date parametrizing mixing for low (<1) Richardson number flows, such as the Equatorial Undercurrent, has received the most attention. Here a new Richardson number parametrization is proposed that provides estimates of vertical turbulent diffusivity in the high Richardson number stratified shear flow that is associated with mesoscale ocean features such as eddies and fronts. This parametrization is based on direct observations of vertical turbulent diffusivity from three separate ocean regions in the North Atlantic and Southern Ocean and is found to be robust for values of the Richardson number greater than 1 at depths below the ocean surface boundary layer. The new parametrization gives substantially improved agreement with the observed mixing in the presence of mesoscale ocean features compared to existing Richardson number parametrizations.