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- Author or Editor: Horacio A. Figueroa x

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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.

## 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.

## Abstract

In this report, the potential for salt finger instability in the central water of the World Ocean is examined. The form of the temperature– salinity relationship determined from the Levitus climatological data and the density ratio of this relationship are used as a proxy to identify the regions that are susceptible to salt finger activity. The analysis indicates that most of the North and South Atlantic basins, and southeastern Indian and southwestern South Pacific Central Waters have density ratios smaller than 2.0. This is an indication that enhanced vertical salinity fluxes due to salt fingers can be an additional process affecting the thermocline freshwater budget. This study also indicates that most of the ocean's central water *T*–*S* curves are better described by a constant density ratio *T*–*S* curve than by a straight line connecting near-surface and intermediate water types.

## Abstract

In this report, the potential for salt finger instability in the central water of the World Ocean is examined. The form of the temperature– salinity relationship determined from the Levitus climatological data and the density ratio of this relationship are used as a proxy to identify the regions that are susceptible to salt finger activity. The analysis indicates that most of the North and South Atlantic basins, and southeastern Indian and southwestern South Pacific Central Waters have density ratios smaller than 2.0. This is an indication that enhanced vertical salinity fluxes due to salt fingers can be an additional process affecting the thermocline freshwater budget. This study also indicates that most of the ocean's central water *T*–*S* curves are better described by a constant density ratio *T*–*S* curve than by a straight line connecting near-surface and intermediate water types.

## Abstract

The Lagrangian and Eulerian descriptions of the flow in a double gyre, eddy-resolving numerical simulation are compared in the context of exploring the use of drifter arrays to describe ocean circulation. The parameterization of the unresolved scales of motion in large-scale numerical ocean models is analyzed through a combination of Lagrangian and Eulerian simulated fields. Here, in Part I, the Lagrangian and Eulerian description of the flow is presented with special emphasis on the description of the eddy diffusivity field. In Part II, the limitations that coarse spatial resolution imposes on the advective–diffusive equation 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 be launched in the Atlantic Ocean during WOCE/TOGA surface velocity program. The parameters that determine the model ocean circulation were chosen 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, from the shear of the velocity field and from the application of Taylor's Lagrangian diffusion theory. This theory relates the absolute dispersion of tagged particles to the diffusive power of the turbulent velocity field in statistically homogeneous and stationary turbulent flows. By using a combination of Lagrangian and Eulerian statistics, it is observed that with a large number of particles the mean Eulerian velocities and velocity variances can be estimated well from the Lagrangian trajectories. The estimation of Lagrangian statistics (i.e., dispersion 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 from the trajectories of the particles released in the eddy-resolving numerical model reproduce the most important large-scale characteristics observed in the analysis of drifters and floats in the ocean: anisotropy of the horizontal components of the diffusivity matrix with zonal values usually being larger than meridional diffusivities, and an inhomogeneous diffusivity field, with large values in those regions where the eddy kinetic energy is larger. Central gyre statistics are typically well defined both in terms of the theory and within the drifter densities used. In the western boundary layer Lagrangian statistics are not robust, not because of sample size problems but due to the breakdown of the assumptions behind single particle calculations. Regimes where this occurs have ratios of the local advective time scale to the Lagrangian decorrelation time scale greater than one and are therefore typically nonstationary.

## Abstract

The Lagrangian and Eulerian descriptions of the flow in a double gyre, eddy-resolving numerical simulation are compared in the context of exploring the use of drifter arrays to describe ocean circulation. The parameterization of the unresolved scales of motion in large-scale numerical ocean models is analyzed through a combination of Lagrangian and Eulerian simulated fields. Here, in Part I, the Lagrangian and Eulerian description of the flow is presented with special emphasis on the description of the eddy diffusivity field. In Part II, the limitations that coarse spatial resolution imposes on the advective–diffusive equation 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 be launched in the Atlantic Ocean during WOCE/TOGA surface velocity program. The parameters that determine the model ocean circulation were chosen 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, from the shear of the velocity field and from the application of Taylor's Lagrangian diffusion theory. This theory relates the absolute dispersion of tagged particles to the diffusive power of the turbulent velocity field in statistically homogeneous and stationary turbulent flows. By using a combination of Lagrangian and Eulerian statistics, it is observed that with a large number of particles the mean Eulerian velocities and velocity variances can be estimated well from the Lagrangian trajectories. The estimation of Lagrangian statistics (i.e., dispersion 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 from the trajectories of the particles released in the eddy-resolving numerical model reproduce the most important large-scale characteristics observed in the analysis of drifters and floats in the ocean: anisotropy of the horizontal components of the diffusivity matrix with zonal values usually being larger than meridional diffusivities, and an inhomogeneous diffusivity field, with large values in those regions where the eddy kinetic energy is larger. Central gyre statistics are typically well defined both in terms of the theory and within the drifter densities used. In the western boundary layer Lagrangian statistics are not robust, not because of sample size problems but due to the breakdown of the assumptions behind single particle calculations. Regimes where this occurs have ratios of the local advective time scale to the Lagrangian decorrelation time scale greater than one and are therefore typically nonstationary.