EDDY RESOLUTION VERSUS EDDY DIFFUSION IN A DOUBLE GYRE GCM .1. THE LAGRANGIAN AND EULERIAN DESCRIPTION

The Lagrangian and Eulerian descriptions of the flow in a double gyre, eddy-resolving numerical simulation are compared in the context of ex ploring the use of drifter arrays to describe ocean circulation. The p arameterization of the unresolved scales of motion in large-scale nume rical ocean models is analyzed through a combination of Lagrangian and Eulerian simulated fields. Here, in Part I, the Lagrangian and Euleri an description of the flow is presented with special emphasis on the d escription of the eddy diffusivity held. In Part II, the limitations t hat coarse spatial resolution imposes on the advective-diffusive equat ion are tested by comparing the evolution of a passive tracer field in high- and low-resolution numerical models. The number of ''buoy days' ' used in the numerical experiment is similar to what is expected to b e launched in the Atlantic Ocean during WOCE/TOGA surface velocity pro gram. The parameters that determine the model ocean circulation were c hosen such that the mean and eddy kinetic energy levels are comparable to observations in the upper ocean. The diffusivity fields presented here are obtained from two different statistical approaches, namely, f rom the shear of the velocity field and from the application of Taylor 's Lagrangian diffusion theory. This theory relates the absolute dispe rsion of tagged particles to the diffusive power of the turbulent velo city field in statistically homogeneous and stationary turbulent flows . By using a combination of Lagrangian and Eulerian statistics, it is observed that with a targe number of particles the mean Eulerian veloc ities and velocity variances can be estimated well from the Lagrangian trajectories. The estimation of Lagrangian statistics (i.e., dispersi on rates with respect to the center of mass, Taylor diffusivities, etc .) depends significantly on the region in which they are computed. The estimation of the spatial distribution of the diffusivity function fr om the trajectories of the particles released in the eddy-resolving nu merical model reproduce the most important large-scale characteristics observed in the analysis of drifters and floats in the ocean: anisotr opy of the horizontal components of the diffusivity matrix with zonal values usually being larger than meridional diffusivities, and an inho mogeneous diffusivity field, with large values in those regions where the eddy kinetic energy is larger. Central gyre statistics are typical ly well defined both in terms of the theory and within the drifter den sities used. In the western boundary layer Lagrangian statistics are n ot robust, not because of sample size problems but due to the breakdow n of the assumptions behind single particle calculations. Regimes wher e this occurs have ratios of the local advective time scale to the Lag rangian decorrelation time scale greater than one and are therefore ty pically nonstationary.