Reconciling float-based and tracer-based estimates of lateral diffusivities

Lateral diffusivities are computed from synthetic particles and tracers advected by a velocity field derived from sea-surface height measurements from the South Pacific, in a region west of Drake Passage. Three different estimates are compared: (1) the tracer-based “effective diffusivity” of Nakamura (1996), (2) the growth of the second moment of a cloud of tracer and (3) the single- and two-particle Lagrangian diffusivities. The effective diffusivity measures the cross-stream component of eddy mixing, so this article focuses on the meridional diffusivities for the others, as the mean flow (the ACC) is zonally oriented in the region. After an initial transient of a few weeks, the effective diffusivity agrees well with the meridional diffusivity estimated both from the tracer cloud and from the particles. This proves that particle- and tracer-based estimates of eddy diffusivities are equivalent, despite recent claims to the contrary. Convergence among the three estimates requires that the Lagrangian diffusivities be estimated using their asymptotic values, not their maximum values. The former are generally much lower than the latter in the presence of a mean flow. Sampling the long-time asymptotic behavior of Lagrangian diffusivities requires very large numbers of floats in field campaigns. For example, it is shown that hundreds of floats would be necessary to estimate the vertical and horizontal variations in eddy diffusivity in a sector of the Pacific Southern Ocean