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High- and medium-resolution satellite optical imagery show that submesoscale cyclonic eddies (SCEs) trap coastal waters and induce their rapid cross-shelf transport. Due to the presence of a rigid boundary, the convergence is observed in the coastal part of SCEs. It causes accumulation of suspended matter, which spins inward in a spiral motion toward the SCE core. Small SCEs with a radius of 1–10 km transport waters with local anomalies in the concentration of chlorophyll, total suspended matter and temperature to a distance of up to 150 km and are observed for more than 10 days. Lagrangian calculations based on realistic NEMO numerical model are used to estimate the fate of the coastal waters in such SCEs. The eddy entrains the largest number of particles during its separation from the coast when its vorticity reaches the maximum. Then, the SCE weakens, which is accompanied by the flattening of initially risen isopycnals and deepening of the trapped coastal waters. The described mechanism shows that coastal SCEs may cause intense short-period cross-shelf transport of the biological and chemical characteristics, and is another process affecting the functioning of the marine ecosystems. [ABSTRACT FROM AUTHOR]

Eddies play a crucial role in shaping ocean dynamics by affecting material transport, and generating spatio‐temporal heterogeneity. However, how eddies at different scales modulate biogeochemical transformation rates remains an open question. Applying a multi‐scale decomposition to a numerical simulation, we investigate the respective impact of mesoscale and submesoscale eddies on nutrient transport and biogeochemical cycling in the California Current System. First, the non‐linear nature of nutrient uptake by phytoplankton results in a 50% reduction in primary production in the presence of eddies. Second, eddies shape the vertical transport of nutrients with a strong compensation between mesoscale and submesoscale. Third, the eddy effect on nutrient uptake is controlled by the covariance of temperature, nutrient and phytoplankton fluctuations caused by eddies. Our results shed new light on the tight interaction between non‐linear fluid dynamics and ecosystem processes in realistic eddy regimes, which remain largely under‐resolved by global Earth system models. Plain Language Summary: Eddies play a crucial role in shaping ocean dynamics by affecting material transport, and generating spatio‐temporal heterogeneity. However, how eddies at different scales modulate biogeochemical transformation rates remains an open question. We address this question in the California Current System, an eddy‐rich, highly productive region. Our method is based on a state‐of‐the‐art high resolution numerical simulation, and employs a multi‐scale decomposition. With this approach, we highlight several key findings that expand our understanding of ocean dynamics and biogeochemistry. First, the transport of nutrients by mesoscale and submesoscale eddies can greatly differ along a gradient of surface nutrient concentrations and circulations. Second, biological nutrient uptake is reduced by about 50% in the presence of eddies. Third, this eddy effect on nutrient uptake is controlled by the covariance of temperature‐nitrogen‐phytoplankton fluctuations at the scale of eddies. These findings challenge the adequacy of non‐eddy resolving models to accurately represent large‐scale biogeochemical transformations. Since the dynamics of pelagic ecosystems is govern by a variety of non‐linear processes, from food‐web interactions to respiration and microbial dynamics, eddy rectification effects could greatly alter ecosystem dynamics and marine habitats, especially in environments naturally sensitive to multiple stressors such as ocean acidification, warming and de‐oxygenation. Key Points: In the California Current, subduction by submesoscale eddies near the coast and mesoscale eddies offshore reduces surface nutrientsIn the presence of submesoscale eddies, the non‐linear nature of nutrient uptake decreases primary production by up to ∼50%The amplitude and sign of eddy nutrient uptake is controlled by the covariance of temperature, nutrient and phytoplankton fluctuations [ABSTRACT FROM AUTHOR]

The North Pacific Gyre Oscillation (NPGO), Pacific Decadal Oscillation, and El Niño‐Southern Oscillation are climate fluctuations in the Pacific. Mesoscale eddies dominate the ocean kinetic energy spectrum. By analyzing the altimetry data, a close linkage between these climate fluctuations and eddy propagation speed is found. Propagation speeds of both cyclonic and anticyclonic eddies in the regions of 10° ∼ 20°N, 120°–180°E and 35° ∼ 45°N, 160°E−160°W are faster in the NPGO negative phase than positive phase, while those in the area of 25° ∼ 35°N, 150°E−170°W are opposite. These differences between positive and negative phases are the response of large‐scale circulation modulated by NPGO. When these climate fluctuations support the same westward/eastward anomaly of circulation, the eddies can propagate much faster/slower than that only considering NPGO. Causality analysis verifies that climate fluctuations can have strong influences on eddy movement. These climate fluctuations can affect the water mass, heat and salt transport by eddy advection. Plain Language Summary: Satellite altimetry is used to investigate the effects of three climate fluctuation including North Pacific Gyre Oscillation, Pacific Decadal Oscillation, and El Niño‐Southern Oscillation on the westward movement of the eddies. It is found that the climate fluctuations affect the eddy westward propagation by regulating the strengthen of large‐scale ocean circulation. Moreover, when the three climate fluctuations support the same westward/eastward anomaly of eddy movement, the intensity of the regulation is greater than that of the single one. Causality analysis also suggests the potential importance of large‐scale climate fluctuations in modulating the eddy motion. This study further indicates that mass, heat and salt transport can be affected by eddy advection modulated these large‐scale climate fluctuations. Key Points: Mesoscale eddies can move faster/slower as a result of the large scale ocean circulation induced by the climate fluctuationsCausality analysis verifies that climate fluctuations can modulate eddy propagation speedLarge scale climate fluctuations can affect the mass, heat and salt transport by eddy advection in the different climate phases [ABSTRACT FROM AUTHOR]

We propose an isoneutral eddy transport diagnostic framework and apply it in the Southern Ocean to analyze eddy potential vorticity (PV) transport dynamics. We leverage a thickness‐weighted spatiotemporal scale separation to define the generalized eddy flux. A local sampling method is employed and validated to estimate the transport tensor. We introduce Leonard's decomposition in Large Eddy Simulations (LES) to split the process into the Reynolds and non‐Reynolds parts. We also use the stationary‐transient decomposition. The non‐Reynolds term and the stationary effect contribute significantly to the transport properties. The Reynolds and transient parts have distinctions, that show oceanic mesoscale dynamics are not synergistic in time and spatial scales. We investigate the spatial scale dependence of each part and find that the transient and stationary components of the Reynolds (non‐Reynolds) term have consistent (dissimilar) scale dependence. The scale dependence of the generalized eddy flux and the transport eigenvalues is controlled by the non‐Reynolds term. We further investigate the eigenvalues in terms of the potential enstrophy and anisotropy. The potential enstrophy in the Southern Ocean holistically has a forward cascade on the researched scales. The Reynolds and transient effects efficiently promote the forward enstrophy cascade. The non‐Reynolds and stationary effects stimulate drastically anisotropic eddy transport. The PV gradient barrier mechanism dominates the drastic anisotropic case. When the anisotropy is weak, a special anisotropic case with a locally balanced potential enstrophy budget overwhelms the case of real isotropy. We also introduce several LES concepts, hoping to enlighten any potential ocean modeling and parameterization. Plain Language Summary: In this study, a 2D spatial filter is applied to define the sub‐grid scale signals or approximately mesoscale eddying signals as the deviation from the filtered large‐scale field. Then, a Reynolds temporal average is used to divide the eddying effect into transient and stationary parts. Since we use a spatial filter to separate the scales, the form of the eddy flux needs to be generalized and a non‐Reynolds part emerges. This part is invisible under the traditional Reynolds average (e.g., zonal average, time average, ensemble average). We introduce Leonard's decomposition from large eddy simulations to decompose the generalized eddy flux into non‐Reynolds and Reynolds parts and to categorize the interactions of eddies with various sizes. We utilize a flux‐gradient relationship to link the generalized eddy flux with the large‐scale tracer gradient through a locally sampled anisotropic transport tensor. Both decompositions and the transport tensor help provide insights into the multiscale nature of mesoscale eddy PV transport dynamics and prompt a theoretical understanding of designing potential LES‐related parameterizations for ocean models. Key Points: A spatiotemporal thickness‐weighted isoneutral eddy transport diagnostic frame‐work is proposed and applied in the Southern OceanThe stationary‐transient and Leonard's decomposition are leveraged to analyze the multiscale effects on eddy potential vorticity transportThe Reynolds and transient effects promote the forward enstrophy cascade, and the non‐Reynolds and stationary effects stimulate anisotropy [ABSTRACT FROM AUTHOR]

The strong interaction between the Brazil Current and the adjacent shelf is clearly visible in satellite‐derived products (sea surface temperature, salinity, and chlorophyll‐a concentration). Assessments of circulation features and cross‐shelf exchanges from these products are, however, limited to the surface layer. Here we analyze the regional circulation and dynamics using the results of a suite of process‐oriented, high‐resolution numerical experiments. Passive tracers and Lagrangian floats characterize the exchanges between the shelf and the open ocean, identifying regions of high variability, and assessing the contribution of small‐scale eddies to the cross‐shelf mass exchanges. We estimate that 0.2–0.4 Sv of the shelf transport variability between 34°S and 25°S comes from ocean internal variability which represents ∼50%–70% of the total variability. Between 25°S and 21°S, internal ocean variability represents more than 90% of the shelf transport variability. We find that generation of cyclonic eddies is more frequent (>15% of the time) at the shelfbreak bights. The core of these eddies contains fresher, colder, and more nutrient‐rich shelf waters. Maps of satellite chlorophyll‐a concentration suggest that the horizontal and vertical exchanges of mass associated with these eddies are a critical element of the primary production cycle. Plain Language Summary: We use the results of a suite of ocean model experiments to investigate the variability of the shelf circulation off southern Brazil and Uruguay and the exchange between the shelf and the open ocean. Ocean internal variability (e.g., from eddies) represents more than 50% of the total shelf transport variability and reaches values up to 90% in the northern shelf region. Supported by maps of satellite chlorophyll‐a and using model passive tracers and Lagrangian floats, we also find that eddies along the shelfbreak play an important role in the advection of colder, fresher, and more nutrient‐rich shelf water to the open‐ocean. This is particularly significant where the shelfbreak changes its orientation (shelfbreak bights) where cyclonic small‐scale eddies are detected more than 15% of the time. Key Points: The variability of the shelf circulation and cross‐shelf exchanges off Southern Brazil and Uruguay is investigated using model experimentsMore than 50% of the total shelf transport variability is explained by internal ocean variabilityEddies along the shelfbreak play an important role in the advection of colder, fresher, and nutrient‐rich shelf water to the open‐ocean [ABSTRACT FROM AUTHOR]

Simple analytic models developed in this study are applied to long‐term averages of reanalysis surface salinity data to quantify two fundamental properties of ocean currents. The first model is based on the new Freshening Length schema and its application to the Irminger Current yields a ratio of about 5 between the turbulent entrainment rates of surrounding fresher surface waters west and east of Greenland. The second model is based on the steady solution of the advection‐diffusion equation subject to suitable boundary conditions. The application of this model to the spreading of fresh, snow‐melt, water from the delta of the Po river in the northwest Adriatic Sea into the rest of the Sea yields a ratio of 8 × 104 m between the eddy exchange coefficient and the speed of advection in the Sea. Plain Language Summary: Differences in ocean water salinity were used for over a century to quantify the horizontal fluxes in and out of evaporative, motionless, basins such as the Mediterranean Sea. In the present study we develop simple expressions based on analytic models that extend the century‐old approach to ocean currents where the water is constantly moving rather than remaining stagnant. The models developed here are combined with long‐term data of sea surface salinity along two currents—the salty Irminger Current that flows around the southern tip of Greenland and the flow of fresh snow‐melt water from the Po river into the Adriatic Sea. The models and climatological data used here yield quantitative estimates of two basic parameters: (a) the rate at which a high‐salinity current detrains salt to the surrounding ocean. (b) The balance between the slow downstream propagation and eddy (turbulent) exchange coefficient. The models developed in this study can be applied to other currents and regions of the world ocean. Key Points: In some oceanic circumstances, changes in Sea Surface Salinity (SSS) gradient provide a simple, reliable and robust diagnostic of ocean currentsChanges in the entrainment rate of surrounding water into a current, correspond to observable changes in SSS gradientReanalysis SSS data quantify the ratio between the speed of advection and the eddy exchange coefficient in slow currents [ABSTRACT FROM AUTHOR]

The heat and momentum flux transfer by transient eddies from the extratropical to the tropical (E2T) region causes a significant variation of weather and climate in the tropical region. Such transports also cause a regional departure from zonally symmetric large scale circulation patterns caused by the Hadley type transports. During boreal summer monsoon season, the zonally symmetric Hadley type circulation is typically considered in theoretical as well as modelling studies. The current study introduces a method based on the calculation of the E‐vector components and co‐spectra analysis to diagnose the zonally asymmetric climatological patterns of E2T transport and its subseasonal variability. The spectral analysis identifies the climatological as well as low and high frequency patterns of the transient eddy heat and momentum flux transfer over the Indian region and compares the result with traditional Eliassen‐Palm (EP) Flux based stationary eddy patterns. The study identifies the zonal, seasonal, and vertical asymmetries in the transport of transient eddy heat and momentum flux. The study also clearly categorizes the seasonality and frequency dependence of northeast to the southwest tilt of transient eddies transporting momentum and heat flux. Based on the climatological patterns, the wavelet transform approach is used to study the subseasonal variability of the eddy transport indices. We define a set of indices, which identify the subseasonal temporal variation of the E2T transfer mechanism. These indices could be used to operationally track the E2T eddy flux transfer both in observation and in forecast models. [ABSTRACT FROM AUTHOR]

The rate of ocean heat uptake depends on the mechanisms that transport heat between the surface and the ocean interior. A recent study found that the vertical heat transport driven by motions with scales smaller than 0.5° (submesoscales) and frequencies smaller than 1 day−1 is upward. This transport competes with the other major components of the global heat transport, namely, the downward heat transport explained by the large‐scale wind‐driven vertical circulation and vertical diffusion at small scales and the upward heat transport associated with mesoscale eddies (50‐ to 300‐km size). The contribution from motions with small spatial scales (<0.5°) and frequencies larger than 1 day−1, including internal gravity waves, has never been explicitly estimated. This study investigates this high‐frequency (subdaily) submesoscale contribution to the global heat transport. The major result of this study, based on the analysis of a high‐resolution ocean model, is that including this high‐frequency contribution surprisingly doubles the upward heat transport due to submesoscales in winter in the global ocean. This contribution typically concerns depths down to 200–500 m and can have a magnitude of up to 500 W m−2 in terms of wintertime heat fluxes at 40‐m depth, which causes a significant upward heat transport of ~7 PW when integrated over the global ocean. Thus, such submesoscale heat transport, which is not resolved by climate models, impacts the heat uptake in the global ocean. The mechanisms involved in these results still need to be understood, which should be the scope of future work. Key Points: Ocean heat flux is large at high frequencySuch high‐frequency flux is generated at submesoscaleSuch heat flux is a key component of global heat budget [ABSTRACT FROM AUTHOR]

Highlights • Thermohaline and dynamic structure of the Black Sea eddies is studied. • Relation of eddy structure on the intensity, life stage and season is described. • Eddies impact on stratification and vertical shear is investigated. • Estimates of vertical velocity in eddies are provided. • Slow down of transport in eddies lead to asymmetry of the basin thermohaline fields. Abstract Combination of altimetry-based method of eddy identification and historical hydrological measurements for 1992–2015 is used to analyze the thermohaline and dynamic structure of the Black Sea eddies and its relation with eddy intensity, eddy age and season of a year. Anticyclonic eddies (AEs) are characterized by negative salinity anomalies, which can reach −1.7 psu at the depth of the main halocline. The temperature anomalies are positive in their upper layers, and negative in the deeper layers, because of the vertical displacement of the waters of the Cold Intermediate Layer (CIL). Cyclonic eddies (CEs) have the opposite structure with increased salinity, colder upper layers and warmer deeper layers. Thermohaline anomalies in the eddies of both signs are maximal in summer, while in winter they are shallowest and minimal. The displacement of pycnocline in eddies causes the decrease/increase of stratification in the upper layer of AEs/CEs and opposite increase/decrease in their deeper layers. It also causes the deepening/uplift of the layer of maximum geostrophic vertical shear in AEs/CEs. The latter is the probable reason of the observed higher intensity and deeper penetration of orbital velocities in AEs than in CEs. The changes of isopycnals positions during the eddies' lifetime are used to quantify the evolution of vertical velocity in AEs and CEs. In the beginning of AEs life during intensification phase, vertical velocity is directed downward, while during the decaying phase it change its sign and is directed upward. The opposite is observed in CEs. Vertical velocity is maximal at the pycnocline depth of 100–110 m with values changing from (−8 to 8) ∗ 10−6 m/s in AEs, and from (+5 to −25) ∗ 10−6 m/s in CEs. Eddies thermohaline structure and altimetry-derived orbital velocity is tightly related. This relation obtained in the study and altimetry-derived data on the distribution of eddy frequency, translational speed and orbital velocity is used to quantify eddies salt, heat content and transport in the basin. The transport velocity of water in the eddies core (2–4 cm/s) is significantly smaller than the average velocity of the large-scale currents (∼10–40 cm/s). Such slowing causes the "relative" transport of eddies against the mean flow direction. This effect leads to the accumulation of brackish and cold water in the deep layers of east Black Sea and maintain the observed east-west asymmetry of the basin thermohaline fields. [ABSTRACT FROM AUTHOR]

Eddies are important not just because they have momentum and can transfer water properties, but also because they play an important role in increasing the trophic energy available to organisms, thereby enhancing primary productivity. This study was conducted to test the ‘suitcase hypothesis’ - the inclusion of organic matter (OM), plankton and larvae within the single water mass of an eddy, which are then highly conserved and transported to another location. Here we hypothesize that particulate OM (POM) and zooplankton from the continental shelf of Madagascar become trapped as the eddy forms and are transported westwards. We analysed stable isotope signatures of POM and zooplankton from samples collected from the continental shelf (CS) as well as within an eddy that had recently formed off the south-west coast of Madagascar. There was no statistical difference in the POM isotopic signature or C/N ratios between the continental shelf or any of the eddy regions. However, some C/N ratio values could suggest that some OM from close to the coastal region could have been transported by the eddy. This was not the case for zooplankton, however, with isotopic signatures on the CS greatly differing from those in the eddy. Several factors could account for these differences including feeding behaviour or tissue turnover rate. We conclude that our study did not gather enough evidence to support (or reject) the ‘suitcase’ hypothesis, and further studies are needed in order to fully understand the transport of material, including zooplankton and larvae, by eddies. [ABSTRACT FROM AUTHOR]

Abstract: Mesoscale anticyclonic eddies are a common feature in the Gulf of Alaska (GOA). A three-dimensional circulation model is used to examine the general characteristics of eddies in the GOA during 1993–2009. Using an eddy detection algorithm, we tracked on average 6.5 eddies formed each year from the modeled results and 6.9 eddies from altimeter data. Modeled eddy characteristics agree with the remote sensing derived eddy statistics in terms of eddy magnitude, propagation speed, and eddy-core diameter. From the model results, strong seasonal and interannual variations were found in both the number and areal coverage of GOA eddies. At the seasonal scale, more eddies are observed to form from March to May, while the eddy-covered area usually peaks around October. At the interannual scale, our results suggest the years with large eddy-covered area do not necessarily have more eddies generated. The long-term variation of eddy-covered area in the GOA is modulated by El Niño/Southern Oscillation (ENSO) events through altering the local wind stress. Model results indicate one typical Haida eddy could transport 37×1018 J of heat and 27km3 of freshwater from the shelf to the central gulf. The equivalent fluxes caused by Haida eddies are comparable with the annual mean of net heat flux and freshwater flux from the atmosphere into the ocean in the Haida region, implying that mesoscale eddies are important sources contributing to the heat and freshwater budgets. [Copyright &y& Elsevier]

This paper considers the formation of the thermohaline structure of the Arctic Ocean: the formation of the salinity field and a freshwater reservoir in the Beaufort Sea and the transport of warm Atlantic water into the central part of the Arctic Ocean. A new version of the Finite Element Model of the Arctic Ocean (FEMAO) with a low spatial resolution is used. The main distinctions of this version are the following features: a new equation of state, a more sophisticated parameterization of vertical turbulence, modified formulations for the boundary conditions on open boundaries (using satellite data on the sea level) and at the upper boundary of the ocean, and the use of a variable eddy diffusivity in the parameterization of the eddy transport of a scalar. Our experiments indicated that the use of the parameterization of the eddy transport of a scalar enhances the transport of warm Atlantic waters to the central part of the Arctic Ocean through the Fram Strait; the results are most realistic when a variable coefficient is used. The Neptune effect has a contradictory role and, in the future, a higher spatial resolution should be used instead of this parameterization. We revealed that a key factor in the thermohaline fields on a large time scale is the interaction with the Atlantic Ocean, which is the source of heat and saline water. [ABSTRACT FROM AUTHOR]

Abstract: Hindcast experiment with an eddy-permitting ocean ecosystem model was performed in order to investigate the process of nutrient supply into the euphotic zone by vertical and horizontal fluxes with multiple time scales. The model reasonably reproduced the basin-scale spatial pattern of biological production and its seasonal cycles with eddy fields, statistically consistent with those observed in the satellite images. The model results illustrated the nutrient cycle in the euphotic zone with mesoscale eddies, in which the vertical advection with mesoscale spatial variation and convection with relatively large spatial variation supply nutrients into the euphotic zone, and the horizontal advection redistributes them within the euphotic zone, thereby fueling biological production. The vertical advection associated with mean flow supplies a substantial part of nutrients from the aphotic zone, and contributions from time-varied vertical fluxes are limited within the tropical region and regions where strong meandering currents exist. Horizontal advection due to seasonal and eddy fluctuations plays an important role in the redistribution process, in addition to that effected by temporal-mean advection. The relative importance of these fluctuations strongly depends on the horizontal scales of vertical nutrient supply, in contrast to the relatively small effects eddy fields have on heat or fresh-water transport in the global ocean. [Copyright &y& Elsevier]

The eddy-induced mass transport is diagnosed for the Southern Ocean in an eddy-permitting global ocean model (OCCAM). The focus is on the transport by transient eddies in the deep ocean. The transport streamfunction is calculated in four different combinations of coordinate system. Depending on the coordinate system employed, the strength of transient eddy transport varies from 6 Sv meridional transport in latitude-density coordinates to 20 Sv across-streamline transport in streamline-depth coordinates. It is shown that transient eddies as well as standing eddies are necessary for cancelling the Deacon cell.In the Antarctic bottom water density layer, the major contribution of the transient eddies towards net equatorward transport occurs (a) as a strong transport over the narrow Drake Passage and (b) as a weaker but systematic transport over a broader region in the southeast Pacific where the Antarctic circumpolar current breaks up into multiple jets. In contrast, in the North Atlantic deep water density layer the net poleward eddy transport is spread out almost everywhere. This suggests that attention to eddies should not be restricted to places where the eddy transport has large magnitude. [Copyright &y& Elsevier]

This study considers the isopycnal eddy transport of mass and passive tracers in eddy-resolving double-gyre quasigeostrophic oceanic circulation. Here we focus on advective transport, whereas a companion paper focuses on eddy-induced diffusive tracer transport. To work towards parameterising eddy tracer transport we quantify the eddy tracer flux using a transport tensor with eddies defined using a spatial filter, which leads to results distinct from those obtained via a temporal Reynolds eddy decomposition. The advection tensor is the antisymmetric part of the transport tensor, and is so named since the associated tracer transport can be expressed as advection of the large-scale tracer field by a rotational eddy-induced velocity (EIV) u ∗ c with streamfunction A. The EIV u ∗ c is fastest (∼ 1 m s−1) where eddy activity is strongest, e.g., in the upper layer, near the eastward jet and western boundary current. Our results suggest that a stochastic closure for the eddy transport would be most suitable since A exhibits a probabilistic distribution when conditioned on, for example, the large-scale relative vorticity. Consistent with closures in ocean circulation models, we quantify eddy mass (isopycnal layer thickness) fluxes as eddy-induced advection by the thickness EIV u ∗ h. The divergent part of u ∗ h – the only part relevant for mass transport in the quasigeostrophic limit – tends to be oriented down the thickness gradient suggesting it quantifies some baroclinic eddy effects similar to those parameterised by the Gent & McWilliams (GM90) EIV. Although u ∗ h has some qualitative similarities to u ∗ c , our results suggest that eddy-induced tracer advection is driven by more than just the thickness-determined EIV and, in turn, more than just the GM90 EIV. • We use spatial filtering methods to separate large-scale and eddy components. • Eddy tracer advection is driven by more than just the thickness-determined eddy-induced velocity. • Eddy mass transport and eddy tracer transport may not be parameterised by the same eddy-induced velocity. • A stochastic closure would be most suitable for parameterising advective eddy transport. [ABSTRACT FROM AUTHOR]

This study provides an interpretation of isopycnal eddy transport for mass and passive tracers in double-gyre eddy-resolving oceanic circulation. This paper focuses on a transport/diffusion tensor representation of the eddy tracer flux, and a companion paper will focus on advective eddy-induced tracer and mass transports. We use a spatial filter to separate the large and small scales, which leads to results distinct from those obtained via a temporal Reynolds eddy decomposition. To work towards a parameterisation, we relate the eddy tracer flux to the large-scale tracer gradient via the transport tensor K. The symmetric part of K is the diffusion tensor, S , which parameterises diffusive fluxes and whose mixing properties are determined by the signs of its eigenvalues. The eigenvalues of S are robustly of opposite sign (polar) and thus quantify filamentation of the tracer via both up- and down-gradient fluxes. Given the prevalence of polar eigenvalues – which are also obtained for Reynolds eddy fluxes – representing their associated effects should be a target of future eddy tracer transport closures. Given the inherent inhomogeneity and anisotropy of the eddy-induced transport, we argue that a full transport tensor is better suited to this task than scalar coefficients or diagonal tensors. The diffusion axis, which represents the direction of preferential mixing, tends to align with the large-scale velocity vector and contours of large-scale relative vorticity and layer thickness. Strong shears can inhibit this alignment. We show that the large-scale velocity gradient matrix may be suitable for parameterising the transport tensor, in particular at depth. Furthermore, since entries of K and S exhibit probabilistic distributions when conditioned on certain large-scale flow features, we suggest that a stochastic closure for the eddy transport would be most suitable. • We use spatial filtering methods to separate large-scale and eddy components. • Eigenvalues of the diffusion tensor are most often of opposite sign. • Eddy tracer diffusion occurs preferentially in the direction of the large-scale flow. • A stochastic closure would be most suitable for parameterising eddy diffusion. [ABSTRACT FROM AUTHOR]