Tracer dispersal by mid-ocean mesoscale eddies. Part I. Ensemble statistics

The rate at which, and the processes by which, a passive tracer is stirred and mixed in a turbulent mesoscale eddy field are examined for environmental parameters characteristic of a homogeneous mid-ocean region. The simulated, time-dependent eddy field is obtained by direct integration of the forced/damped barotropic vorticity equation; the dispersal of a spatially localized, instantaneous release of tracer (a “tracer spot”) within the evolving velocity field is subsequently computed from the advective-diffusive equation. An ensemble of 10 independent releases is used to determin the average spreading properties of the tracer spot.On an f-plane, the ensemble-averaged dispersal is approximately isotropic, and is associated with an effective diffusion rate substantially greater than that supported in the absence of turbulent advection. Quantitatively, the effective ensemble-averaged diffusivity is shown to be 0(UL), where U and L are characteristic velocity and length scales of the turbulent flow. This estimate is consistent with the traditional mixing length hypothesis. With the addition of β, the simulated flow field has substantial zonal anisotropy. Ensemble-averaged dispersal of tracer spots is similarly anisotropic, and the overall rate of tracer dispersal is substantially reduced over its f-plane value.Both with and without β, the initial rate at which maximum tracer concentration and total tracer variance decay are given by the approximate law exp? αγt] where γ is the RMS rate of strain, and α is approximately constant at a value of 0.5. The heightened rate of variance loss over that associated with pure (subgridscale) diffusion is shown to be accommodated by the rapid transfer of tracer variance from the largest to the shortest scale tracer features, that is, by the rapid sharpening of tracer gradients by turbulent advection. A detailed examination of the dispersal of individual tracer realizations, and the associated question of tracer streakiness, is given in part II of this work (Keffer and Haidvogel, in preparation).