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Geostrophic eddies contribute to the mixing of heat, carbon, and other climatically important tracers. A passive tracer driven by satellite-derived surface velocity fields is used to study the regional and temporal variability of lateral eddy mixing in the North Atlantic. Using a quasi-Lagrangian diffusivity diagnostic, we show that the upstream region (80°–50°W) of the Gulf Stream jet exhibits a significant mixing barrier (with diffusivity of ≈1 × 103 m2 s−1), compared to the downstream region (50°–10°W), which displays no mixing suppression (≈10 × 103 m2 s−1). The interannual variability is 10%–20% of the time mean in both regions. By analyzing linear perturbations of mixing-length diffusivity expression, we show that the across-jet mixing in the upstream region is driven by variations in the mean flow, rather than eddy velocity. In the downstream region, both the mean flow and eddy velocity contribute to the temporal variability. Our results suggest that an eddy parameterization must take into account the along-jet variation of mixing, and within jets such diffusivities may be a simple function of jet strength.

It has been hypothesized that submesoscale flows play an important role in the vertical transport of climatically important tracers, due to their strong associated vertical velocities. However, the multi-scale, non-linear, and Lagrangian nature of transport makes it challenging to attribute proportions of the tracer fluxes to certain processes, scales, regions, or features. Here we show that criteria based on the surface vorticity and strain joint probability distribution function (JPDF) effectively decomposes the surface velocity field into distinguishable flow regions, and different flow features, like fronts or eddies, are contained in different flow regions. The JPDF has a distinct shape and approximately parses the flow into different scales, as stronger velocity gradients are usually associated with smaller scales. Conditioning the vertical tracer transport on the vorticity-strain JPDF can therefore help to attribute the transport to different types of flows and scales. Applied to a set of idealized Antarctic Circumpolar Current simulations that vary only in horizontal resolution, this diagnostic approach demonstrates that small-scale strain dominated regions that are generally associated with submesoscale fronts, despite their minuscule spatial footprint, play an outsized role in exchanging tracers across the mixed layer base and are an important contributor to the large-scale tracer budgets. Resolving these flows not only adds extra flux at the small scales, but also enhances the flux due to the larger-scale flows.

A suite of observationally driven model experiments is used to investigate the contribution of near-surface lateral eddy mixing to the subtropical surface salinity maxima in the global ocean. Surface fields of salinity are treated as a passive tracer and stirred by surface velocities derived from altimetry, leading to irreversible water-mass transformation. In the absence of surface forcing and vertical processes, the transformation rate can be directly related to the integrated diffusion across tracer contours, which is determined by the observed velocities. The destruction rates of the salinity maxima by lateral mixing can be compared to the production rates by surface forcing, which act to strengthen the maxima. The ratio of destruction by eddy mixing in the surface layer versus the surface forcing exhibits regional differences in the mean—from 10% in the South Pacific to up to 25% in the south Indian. Furthermore, the regional basins show seasonal and interannual variability in eddy mixing. The dominant mechanism for this temporal variability varies regionally. Most notably, the North Pacific shows a large sensitivity to the background salinity fields and a weak sensitivity to the velocity fields, while the North Atlantic exhibits the opposite behavior. The different mechanism for temporal variability could have impacts on the manifestation of a changing hydrological cycle in the sea surface salinity (SSS) field specifically in the North Pacific. The authors find evidence for large-scale interannual changes of eddy diffusivity and transformation rate in several ocean basins that could be related to large-scale climate forcing.

The transport by materially coherent surface-layer eddies was studied in a two-layer quasigeostrophic model driven by eastward mean shear. The coherent eddies were identified by closed contours of the Lagrangian-averaged vorticity deviation obtained from Lagrangian particles advected by the flow. Attention was restricted to eastward mean flows, but a wide range of flow regimes with different bottom friction strengths, layer thickness ratios, and background potential vorticity (PV) gradients were otherwise considered. It was found that coherent eddies become more prevalent and longer-lasting as the strength of bottom drag increases and the stratification becomes more surface-intensified. The number of coherent eddies is minimal when the shear-induced PV gradient is 10&ndash, 20 times the planetary PV gradient and increases for both larger and smaller values of the planetary PV gradient. These coherent eddies, with an average core radius close to the deformation radius, propagate meridionally with a preference for cyclones to propagate poleward and anticyclones to propagate equatorward. The meridional propagation preference of the coherent eddies gives rise to a systematic upgradient PV transport, which is in the opposite direction as the background PV transport and not captured by standard Lagrangian diffusivity estimates. The upgradient PV transport by coherent eddy cores is less than 15% of the total PV transport, but the PV transport by the periphery flow induced by the PV inside coherent eddies is significant and downgradient. These results clarify the distinct roles of the trapping and stirring effect of coherent eddies in PV transport in geophysical turbulence.

An idealized eddy-resolving ocean basin, closely resembling the North Pacific ocean, is simulated using MITgcm. We identify rotationally coherent Lagrangian vortices (RCLVs) and sea surface height (SSH) eddies based on the Lagrangian and Eulerian framework, respectively. General statistical results show that RCLVs have a much smaller coherent core than SSH eddies with the ratio of radius is about 0.5. RCLVs are often enclosed by SSHA contours, but SSH eddy identification method fails to detect more than half of RCLVs. Based on their locations, two types of eddies are classified into three categories: overlapping RCLVs and SSH eddies, non-overlapping SSH eddies, and non-overlapping RCLVs. Using Lagrangian particles, we examine the processes of leakage and intrusion around SSH eddies. For overlapping SSH eddies, over the lifetime, the material coherent core only accounts for about 25%, and about 50% of initial water leak from eddy interior. The remaining 25% of water can still remain inside the boundary, but only in the form of filaments outside the coherent core. For non-overlapping SSH eddies, more water leakage (about 60\%) occurs at a faster rate. Following the number and radius of real SSH eddies, fixed circles and moving circles are randomly selected to diagnose the material flux around these circles. We find that the leakage and intrusion trends of moving circles are quite similar to that of non-overlapping SSH eddies, suggesting that the material coherence properties of non-overlapping SSH eddies are not significantly different from random pieces of ocean with the same size.

Stratification in the Southern Ocean is determined primarily by a competition between westerly wind-driven upwelling and baroclinic eddy transport. This study investigates the time scales of equilibration of the Southern Ocean in response to changing winds through an idealized channel model. An analytical framework describing the energetic pathways between wind input, available potential energy (APE), eddy kinetic energy (EKE), and dissipation provides a simple theory of the phase and amplitude response to oscillating wind stress. The transient ocean response to variable winds lies between the two limits of Ekman response (high frequency), characterized by the isopycnal slope responding directly to wind stress, and “eddy saturation” (low frequency), wherein a large fraction of the anomalous wind work goes into mesoscale eddies. The crossover time scale is the time scale of meridional eddy diffusive transport across the Antarctic Circumpolar Current (ACC) front. For wind variability with a period of 3 months (high-frequency forcing), the relative conversion of wind work to APE/EKE is 11, while for a period of 16 years (low-frequency forcing), the relative conversion to APE/EKE reduces to 3. The system’s frequency response is characterized by a complex transfer function. Both the phase and amplitude response of EKE and APE predicted by the linear analytic framework are verified using multiple ensemble experiments in an eddy-resolving (4-km horizontal resolution) isopycnal coordinate model. The results from the numerical experiments show agreement with the linear theory and can be used to explain certain features observed in previous modeling studies and observations.

The phase speed spectrum of ocean mesoscale eddies is fundamental to understanding turbulent baroclinic flows. Since eddy phase propagation has been shown to modulate eddy fluxes, an understanding of eddy phase speeds is also of practical importance for the development of improved eddy parameterizations for coarse resolution ocean models. However, it is not totally clear whether and how linear Rossby wave theory can be used to explain the phase speed spectra in various weakly turbulent flow regimes. Using linear analysis, theoretical constraints are identified that control the eddy phase speed in a two-layer quasigeostrophic (QG) model. These constraints are then verified in a series of nonlinear two-layer QG simulations, spanning a range of parameters with potential relevance to the ocean. In the two-layer QG model, the strength of the inverse cascade exerts an important control on the eddy phase speed. If the inverse cascade is weak, the phase speed spectrum is reasonably well approximated by the phase speed of the linearly most unstable mode. A significant inverse cascade instead leads to barotropization, which in turn leads to mean phase speeds closer to those of barotropic-mode Rossby waves. The two-layer QG results are qualitatively consistent with the observed eddy phase speed spectra in the Antarctic Circumpolar Current and may also shed light on the interpretation of phase speed spectra observed in other regions.

This study investigates the observed spectral character of eddy heat fluxes near the ocean surface, focusing on the distribution in wavenumber and phase speed space. Eddy heat fluxes in the eastern Pacific are calculated from concurrent satellite sea surface height and sea surface temperature data. A high-resolution coupled climate model is also analyzed in order to verify the physical mechanisms involved and to validate the model against observations. Wavenumber, frequency, and phase speed power spectra and cross spectra are constructed and presented as a function of latitude. These spectra reveal the dominance of coherent mesoscale eddies in both the length scale and phase speed of eddy heat fluxes. The breadths of the spectra are characterized via spectral moments; these moments show that the eddy fluxes are relatively concentrated around the dominant wavenumber and phase speed. Good agreement is found between the model and the observed spectra. The integrated heat transport and corresponding eddy diffusivity are shown to compare well with previous studies, but the results give a deeper insight into what determines the heat flux. Implications for eddy parameterization are discussed.

The processes that determine the depth of the Southern Ocean thermocline are considered. In existing conceptual frameworks, the thermocline depth is determined by competition between the mean and eddy heat transport, with a contribution from the interaction with the stratification in the enclosed portion of the ocean. Using numerical simulations, this study examines the equilibration of an idealized circumpolar current with and without topography. The authors find that eddies are much more efficient when topography is present, leading to a shallower thermocline than in the flat case. A simple quasigeostrophic analytical model shows that the topographically induced standing wave increases the effective eddy diffusivity by increasing the local buoyancy gradients and lengthening the buoyancy contours across which the eddies transport heat. In addition to this local heat flux intensification, transient eddy heat fluxes are suppressed away from the topography, especially upstream, indicating that localized topography leads to local (absolute) baroclinic instability and its subsequent finite-amplitude equilibration, which extracts available potential energy very efficiently from the time-mean flow.

Mesoscale eddies mix tracers along isopycnals and horizontally at the sea surface. This paper compares different methods of diagnosing eddy mixing rates in an idealized, eddy-resolving model of a channel flow meant to resemble the Antarctic Circumpolar Current. The first set of methods, the ''perfect'' diag- nostics, are techniques suitable only to numerical models, in which detailed synoptic data is available. The perfect diagnostic include flux-gradient diffusivities of buoyancy, QGPV, and Ertel PV; Nakamura effective diffusivity; and the four-element diffusivity tensor calculated from an ensemble of passive tracers. These diagnostics reveal a consistent picture of isopycnal mixing by eddies, with a pronounced maximum near 1000 m depth. The isopycnal diffusivity differs from the buoyancy diffusivity, a.k.a. the Gent-McWilliams transfer coefficient, which is weaker and peaks near the surface and bottom. The sec- ond set of methods are observationally ''practical'' diagnostics. They involve monitoring the spreading of tracers or Lagrangian particles in ways that are plausible in the field. We show how, with sufficient ensemble size, the practical diagnostics agree with the perfect diagnostics in an average sense. Some implications for eddy parameterization are discussed.

Rotationally coherent Lagrangian vortices (RCLVs) are identified from satellite-derived surface geostrophic velocities in the eastern Pacific (180°–130°W) using the objective (frame invariant) finite-time Lagrangian coherent structure detection method of Haller et al. based on the Lagrangian-averaged vorticity deviation. RCLVs are identified for 30-, 90-, and 270-day intervals over the entire satellite dataset, beginning in 1993. In contrast to structures identified using Eulerian eddy-tracking methods, the RCLVs maintain material coherence over the specified time intervals, making them suitable for material transport estimates. Statistics of RCLVs are compared to statistics of eddies identified from sea surface height (SSH) by Chelton et al. RCLVs and SSH eddies are found to propagate westward at similar speeds at each latitude, consistent with the Rossby wave dispersion relation. However, RCLVs are uniformly smaller and shorter-lived than SSH eddies. A coherent eddy diffusivity is derived to quantify the contribution of RCLVs to meridional transport; it is found that RCLVs contribute less than 1% to net meridional dispersion and diffusion in this sector, implying that eddy transport of tracers is mostly due to incoherent motions, such as swirling and filamentation outside of the eddy cores, rather than coherent meridional translation of eddies themselves. These findings call into question prior estimates of coherent eddy transport based on Eulerian eddy identification methods.

[1] Velocities derived from AVISO sea-surface height observations, adjusted to be nondivergent, are used to simulate the evolution of passive tracers at the ocean surface. Eddy mixing rates are derived from the tracer fields in two ways. First, the method of Nakamura is applied to a sector in the East Pacific. Second, the Osborn-Cox diffusivity is calculated globally to yield estimates of diffusivity in two dimensions. The results from the East Pacific show weak meridional mixing at the surface in the Southern Ocean (

The Southern Ocean’s Antarctic Circumpolar Current (ACC) and meridional overturning circulation (MOC) response to increasing zonal wind stress is, for the first time, analyzed in a high-resolution (0.1° ocean and 0.25° atmosphere), fully coupled global climate simulation using the Community Earth System Model. Results from a 20-yr wind perturbation experiment, where the Southern Hemisphere zonal wind stress is increased by 50% south of 30°S, show only marginal changes in the mean ACC transport through Drake Passage—an increase of 6% [136–144 Sverdrups (Sv; 1 Sv ≡ 106 m3 s−1)] in the perturbation experiment compared with the control. However, the upper and lower circulation cells of the MOC do change. The lower cell is more affected than the upper cell with a maximum increase of 64% versus 39%, respectively. Changes in the MOC are directly linked to changes in water mass transformation from shifting surface isopycnals and sea ice melt, giving rise to changes in surface buoyancy forcing. The increase in transport of the lower cell leads to upwelling of warm and salty Circumpolar Deep Water and subsequent melting of sea ice surrounding Antarctica. The MOC is commonly supposed to be the sum of two opposing components: a wind- and transient-eddy overturning cell. Here, the transient-eddy overturning is virtually unchanged and consistent with a large-scale cancellation of localized regions of both enhancement and suppression of eddy kinetic energy along the mean path of the ACC. However, decomposing the time-mean overturning into a time- and zonal-mean component and a standing-eddy component reveals partial compensation between wind-driven and standing-eddy components of the circulation.

A perceived limitation of z-coordinate models associated with spurious diapycnal mixing in eddying, frontal flow, can be readily addressed through appropriate attention to the tracer advection schemes employed. It is demonstrated that tracer advection schemes developed by Prather and collaborators for application in the stratosphere, greatly improve the fidelity of eddying flows, reducing levels of spurious diapycnal mixing to below those directly measured in field experiments, ∼1 × 10⁻⁵ m² s⁻¹. This approach yields a model in which geostrophic eddies are quasi-adiabatic in the ocean interior, so that the residual-mean overturning circulation aligns almost perfectly with density contours. A reentrant channel configuration of the MIT General Circulation Model, that approximates the Antarctic Circumpolar Current, is used to examine these issues. Virtual analogs of ocean deliberate tracer release field experiments reinforce our conclusion, producing passive tracer solutions that parallel field experiments remarkably well.

An eddy-resolving numerical model of a zonal flow, meant to resemble the Antarctic Circumpolar Current, is described and analyzed using the framework of J. Marshall and T. Radko. In addition to wind and buoyancy forcing at the surface, the model contains a sponge layer at the northern boundary that permits a residual meridional overturning circulation (MOC) to exist at depth. The strength of the residual MOC is diagnosed for different strengths of surface wind stress. It is found that the eddy circulation largely compensates for the changes in Ekman circulation. The extent of the compensation and thus the sensitivity of the MOC to the winds depend on the surface boundary condition. A fixed-heat-flux surface boundary severely limits the ability of the MOC to change. An interactive heat flux leads to greater sensitivity. To explain the MOC sensitivity to the wind strength under the interactive heat flux, transformed Eulerian-mean theory is applied, in which the eddy diffusivity plays a central role in determining the eddy response. A scaling theory for the eddy diffusivity, based on the mechanical energy balance, is developed and tested; the average magnitude of the diffusivity is found to be proportional to the square root of the wind stress. The MOC sensitivity to the winds based on this scaling is compared with the true sensitivity diagnosed from the experiments.

Meridional cross sections of effective diffusivity in the Southern Ocean are presented and discussed. The effective diffusivity, Keff, characterizes the rate at which mesoscale eddies stir properties on interior isopycnal surfaces and laterally at the sea surface. The distributions are obtained by monitoring the rate at which eddies stir an idealized tracer whose initial distribution varies monotonically across the Antarctic Circumpolar Current (ACC). In the absence of observed maps of eddying currents in the interior ocean, the advecting velocity field is taken from an eddy-permitting state estimate of the Southern Ocean (SOSE). A three-dimensional advection–diffusion equation is solved and the diffusivity diagnosed by applying the Nakamura technique on both horizontal and isopycnal surfaces. The resulting meridional sections of Keff reveal intensified isopycnal eddy stirring (reaching values of ∼2000 m2 s−1) in a layer deep beneath the ACC but rising toward the surface on the equatorward flank. Lower effective diffusivity values (∼500 m2 s−1) are found near the surface where the mean flow of the ACC is strongest. It is argued that Keff is enhanced in the vicinity of the steering level of baroclinic waves, which is deep along the axis of the ACC but shallows on the equatorial flank. Values of Keff are also found to be spatially correlated with gradients of potential vorticity on isopycnal surfaces and are large where those gradients are weak and vice versa, as expected from simple dynamical arguments. Finally, implications of the spatial distributions of Keff for the dynamics of the ACC and its overturning circulation are discussed.

Anthropogenic carbon dioxide uptake varies across Earth System Models for reasons that have remained obscure. When varied within a single model, the lateral eddy mixing coefficient ARedi produces a range of uptake similar to the modeled range. The highest uptake, resulting from a simulation with a constant ARedi of 2400 m2/s, simulates 15% more historical carbon uptake than a model with ARedi = 400 m2/s. A sudden doubling in carbon dioxide produces a 21% range in carbon uptake across the models. Two spatially dependent representations of ARedi produce uptake that lies in the middle of the range of constant values despite predicting very large values in the subtropical gyres. One-dimensional diffusive models of the type used for integrated assessments can be fit to the simulations, with ARedi accounting for a substantial fraction of the effective vertical diffusion. Such models, however, mask significant regional changes in stratification and biological carbon storage.