A diagnosis of isopycnal mixing by mesoscale eddies

Combining the buoyancy and tracer budget in the generalised Temporal Residual Mean (TRM-G) framework of [Eden, C., Greatbatch, R.J., Olbers, D. 2007a. Interpreting eddy fluxes. J. Phys. Oceanogr. 37, 1282–1296], we show that within the small slope approximation and weakly diabatic situation, the isopycnal diffusivity is related to the difference of the streamfunctions of the eddy-induced velocities of tracer and buoyancy divided by the angle between the (negative) slopes of isopycnals and the isolines of the tracer. Using this result tracer simulations of a realistic mesoscale-eddy-permitting model of the North Atlantic coupled to a biogeochemical model are diagnosed in terms of zonal (KI(x)) and meridional (KI(y)) isopycnal diffusivities relevant for non-eddy-permitting ocean models.We find for tracers having different interior sources and surface forcing and therefore different lateral and vertical mean gradients, values of KI(x) and KI(y) with similar magnitudes and lateral and vertical structure. In general, isopycnal diffusivities lie within the expected range between 0 and 5000 m2/s but we also find a strong anisotropy with KI(x) much larger than KI(y) over large regions of the North Atlantic. Both KI(x) and KI(y) are larger within and above the thermocline but decay almost to zero below. Our results also support the common practise of the use of identical isopycnal and thickness diffusivity for any tracer in ocean models.