Eddy Resolution versus Eddy Diffusion in a Double Gyre GCM. Part II: Mixing of Passive Tracers

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Abstract
The parameterization of the effect of the unresolved scales of motion on a passive tracer field in large-scale numerical ocean models is analyzed through a combination of Lagrangian and Eulerian velocities. The primitive equation isopycnal model discussed by Bleck and Boudra is used in Part I to simulate the trajectory of particles in an eddy-resolving double gyre circulation. From these trajectories, and from the associated Eulerian velocity field, a Lagrangian isopycnal diffusivity field and a deformation-dependent diffusivity distribution were estimated (Part I). Here (Part II), the same velocity field is used to simulate the evolution of idealized passive tracer fields in fine (20 km) and coarse (200 km) resolution models. The main goal of this work is to test the limitations that coarse horizontal resolution imposes on the advective–diffusive equation by comparing the evolution of a passive tracer field in a high-resolution version of the model and in an “off line” version. This off-line velocity field is meant to represent the velocity resulting from a coarse spatial resolution simulation. The model ocean is represented by a typical double gyre circulation thoroughly presented in the literature. The consistency in the comparison of the evolution of various tracer fields from the high- and coarse-resolution simulations is anticipated by parameterizing the eddy diffusivity field in the coarse-resolution model with an eddy diffusivity distribution obtained from the eddy velocity field in the high-resolution version of the model. Likewise, the advective velocity field used to represent the velocity from a coarse-resolution models is the Eulerian mean velocity field estimated from the eddy-resolving model. The evolution of the tracer field in the eddy-resolving experiment is analyzed in terms of the tracer mixing across the model subpolar and subtropical gyres. It is observed that the intergyre tracer exchange is the result of three main mechanisms: the subgrid-scale diffusivity, the transport of anomalous tracers trapped during the formation (and shedding) of eddies, and the occurrence of a phase shift between the meandering streamlines and the meander formed by the tracer front. The coarse-resolution tracer simulations presented here indicate that there is no eddy diffusivity field consistently determined that when combined with a coarse advective velocity field can totally reproduce the tracer distribution and the meridional tracer fluxes comparable to those obtained from the eddy-resolving version of the model. These simulations suggest, however, that the use of a spatially dependent horizontal diffusivity field greatly improves the accuracy of the passive tracer simulations (compared to the eddy-resolving simulations) over the use of a constant eddy diffusion coefficient.

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