Robustness of an Effective Diffusivity Diagnostic in Oceanic Flows

Abstract

The robustness of Nakamura’s effective diffusivity diagnostic for quantifying eddy diffusivities of tracers within a streamwise-average framework is carefully examined in an oceanographic context, and the limits of its applicability are detailed. The near-surface Southern Ocean geostrophic flow, obtained from altimetric observations, is chosen for particular examination since it exhibits strong eddy activity. Careful analysis indicates that the effective diffusivity calculation is not strongly sensitive to the resolution of the velocity field or to the tracer initial conditions (after a spinup time of 3 months), and that a numerical diffusivity of 50 m[superscript 2] s[superscript −1] is appropriate to resolve the Batchelor scale at a computational resolution of 1/20°. The spatial variability of the effective diffusivity is examined and shown to be related to the eddy kinetic energy (EKE), mean zonal current (u), and phase speed of the eddies (c), following the streamwise averge of EKE/(u − c)[superscript 2], in agreement with linear baroclinic instability theory. The temporal variability of the effective diffusivity over the period 1996–2001 indicates significant variability on seasonal time scales with a magnitude of ±10%–15%. Interannual variations are investigated and discussed in the context of changes in the wind stress associated with the southern annular mode.