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Oceanic macroturbulence is efficient at stirring and transporting tracers. The dynamical properties of this stirring can be characterized by statistically quantifying tracer structures. Here, we characterize the macroscale (1-100 km) tracer structures observed by two Seagliders downstream of the Southwest Indian Ridge (SWIR) in the Antarctic Circumpolar Current (ACC). These are some of the first glider observations in an energetic standing meander of the ACC, regions associated with enhanced ventilation. The small-scale density variance in the mixed layer (ML) was relatively enhanced near the surface and base of the ML, while being muted in the middle, suggesting the formation mechanism to be associated to ML instabilities and eddies. In addition, ML density fronts were formed by comparable contributions from temperature and salinity gradients, suggesting the dominant role of stirring, over air-sea interactions, in their formation and sustainability. In the interior, along-isopycnal spectra and structure functions of spice indicated that there is relatively lower variance at smaller scales than would be expected based on non-local stirring, suggesting that flows smaller than the deformation radius play a role in the cascade of tracers to small scales. These interior spice anomalies spanned across isopycnals, and were found to be about 3-5 times flatter than the aspect ratio that would be expected for O(1) Burger number flows like interior QG dynamics, suggesting the ratio of vertical shear to horizontal strain is greater than $N/f$. This further supports that small-scale flows, with high-mode vertical structures, stir tracers and impact tracer distributions.

The anisotropic mesoscale eddy transport tensor is diagnosed using passive tracers advected in both an idealized 101-member mesoscale-resolving quasi-geostrophic (QG) double-gyre ensemble, and a realistic 24-member eddying ($1/12^\circ$) ensemble of the North Atlantic. We assert that the Reynold's decomposition along the ensemble dimension, rather than the spatial or temporal dimension, allows us to capture the intrinsic spatiotemporal variability of the mean flow and eddies.The tensor exhibits good performance in reconstructing the eddy fluxes of passive tracers, here defined as fluctuations about the ensemble thickness-weighted averaged (TWA) mean.However, the inability of the tensor to reconstruct eddy fluxes of QG potential vorticity, which encapsulates the eddy-mean flow interaction, and other active tracers raises the question: To what extent can the diagnosed tensor be applied to inform the parametrization of mesoscale dynamics?

Slowly evolving stratified flow over rough topography is subject to substantial drag due to internal motions, but often numerical simulations are carried out at resolutions where this “wave” drag must be parameterized. Here we highlight the importance of internal drag from topography with scales that cannot radiate internal waves, but may be highly nonlinear, and we propose a simple parameterization of this drag that has a minimum of fit parameters compared to existing schemes. The parameterization smoothly transitions from a quadratic drag law () for low Nh/u0 (linear wave dynamics) to a linear drag law () for high Nh/u0 flows (nonlinear blocking and hydraulic dynamics), where N is the stratification, h is the height of the topography, and u0 is the near-bottom velocity; the parameterization does not have a dependence on Coriolis frequency. Simulations carried out in a channel with synthetic bathymetry and steady body forcing indicate that this parameterization accurately predicts drag across a broad range of forcing parameters when the effect of reduced near-bottom mixing is taken into account by reducing the effective height of the topography. The parameterization is also tested in simulations of wind-driven channel flows that generate mesoscale eddy fields, a setup where the downstream transport is sensitive to the bottom drag parameterization and its effect on the eddies. In these simulations, the parameterization replicates the effect of rough bathymetry on the eddies. If extrapolated globally, the subinertial topographic scales can account for 2.7 TW of work done on the low-frequency circulation, an important sink that is redistributed to mixing in the open ocean.

Flow-topography interactions along the path of the Antarctic Circumpolar Current generate standing meanders, create regions of enhanced eddy kinetic energy (EKE), and modify frontal structure. We consider the impact of standing meanders on ventilation based on oxygen measurements from Argo floats and the patterns of apparent oxygen utilization (AOU). Regions of high-EKE have relatively reduced AOU values at depths 200–700 m below the base of the mixed layer and larger AOU variance, suggesting enhanced ventilation due to both along-isopycnal stirring and enhanced exchange across the base of the mixed layer. Vertical exchange is inferred from finite-size Lyapunov exponents, a proxy for the magnitude of surface lateral density gradients, which suggest that submesoscale vertical velocities may contribute to ventilation. The shaping of ventilation by standing meanders has implications for the temporal and spatial variability of air‒sea exchange.

Ocean turbulence causes flows to split into smaller whirls or merge to make larger whirls, cascading energy to small or large scales respectively. Conventional ocean dynamics dictates that the kinetic energy in the ocean will cascade primarily to larger scales, via the inverse energy cascade, and has raised the question of how the kinetic energy in the ocean dissipates, which would necessarily require the transfer towards the molecular scales. However, so far no clear observational quantification of the energy cascade at the scales where these mechanisms are potentially active has been made. By using forcing-scale resolving third-order structure-function theory, which captures bidirectional energy fluxes and is applicable beyond inertial ranges, we analyse data from surface drifters, released in dense arrays in the Gulf of Mexico, to obtain the kinetic energy flux magnitude and directions along with the energy injection scales. We provide the first direct observational verification that the surface kinetic energy cascades to both small and large scales, with the forward cascade dominating at scales smaller than approximately 1-10km. Our results also show that there is a seasonality in these cascades, with winter months having a stronger injection of energy into the surface flows and a more energetic cascade to smaller scales. This work provides exciting new opportunities for further probing the energetics of ocean turbulence using non-gridded sparse observations, such as from drifters, gliders, or satellites.

The analysis of eddy-mean flow interaction provides key insights into the structures and dynamics of inhomogeneous and anisotropic flows such as atmospheric and oceanic jets. As the divergence of Eliassen-Palm (E-P) flux formally encapsulates the interaction, the community has had a long-standing interest in accurately diagnosing this term. Here, we revisit the E-P flux divergence with an emphasis on the Gulf Stream, using a 48-member, eddy-rich (1/12°) ensemble of the North Atlantic ocean partially coupled to identical atmospheric states amongst all members via an atmospheric boundary layer model. This dataset allows for an unique decomposition where we define the mean flow as the ensemble mean, and interpret it as the oceanic response to the atmospheric state. The eddies are subsequently defined as fluctuations about the ensemble mean. Our results highlight two points: i) the implementation of the Thickness-Weighted Averaged (TWA) framework for a realistic ocean simulation in diagnosing the E-P flux divergence, and ii) validity of the ergodic assumption where one treats the temporal mean equivalent to the ensemble mean, which is questionable for a temporally varying system such as the ocean and climate.

The Ocean's turbulent energy cycle has a paradox; large-scale eddies under the control of Earth's rotation primarily transfer kinetic energy (KE) to larger scales via an inverse cascade, while a transfer to smaller scales is needed to accomplish dissipation. It has been argued, using numerical simulations, that fronts, waves and other turbulent structures can produce a forward cascade of KE toward dissipation scales. However, this forward cascade and its coexistence with known inverse cascade were not confirmed in observations. Here we present the first evidence of a dual KE cascade in the Ocean by analyzing velocity measurements from surface drifters released in the Gulf of Mexico. Our results show that KE is injected at two dominant scales and transferred to both large and small scales, with the downscale flux dominating at scales smaller than ~1-10km. The cascade rates are modulated seasonally, with stronger KE injection and forward transfer during winter., Comment: No comments

The thickness-weighted average (TWA) framework, which treats the residual-mean flow as the prognostic variable, provides a clear theoretical formulation of the eddy feedback onto the residual-mean ...

We investigate the role of small‐scale, high‐frequency motions on lateral transport in the ocean, by using velocity fields and particle trajectories from an ocean general circulation model (MITgcm‐llc4320) that permits submesoscale flows, inertia‐gravity waves, and tides. Temporal averaging/filtering removes most of the submesoscale turbulence, inertia‐gravity waves, and tides, resulting in a largely geostrophic flow, with a rapid drop‐off in energy at scales smaller than the mesoscales. We advect two types of Lagrangian particles: (a) 2‐D particles (surface restricted) and (b) 3‐D particles (advected in full three dimensions) with the filtered and unfiltered velocities and calculate Lagrangian diagnostics. At large length/time scales, Lagrangian diffusivity is comparable for filtered and unfiltered velocities, while at short scales, unfiltered velocities disperse particles much faster. We also calculate diagnostics of Lagrangian coherent structures:rotationally coherent Lagrangian vortices detected from closed contours of the Lagrangian‐averaged vorticity deviation and material transport barriers formed by ridges of maximum finite‐time Lyapunov exponent. For temporally filtered velocities, we observe strong material coherence, which breaks down when the level of temporal filtering is reduced/removed, due to vigorous small‐scale mixing. In addition, for the lowest temporal resolution, the 3‐D particles experience very little vertical motion, suggesting that degrading temporal resolution greatly reduces vertical advection by high‐frequency motions. Our study suggests that Lagrangian diagnostics based on satellite‐derived surface geostrophic velocity fields, even with higher spatial resolutions as in the upcoming Surface Water and Ocean Topography mission, may overestimate the presence of mesoscale coherent structures and underestimate dispersion.

With the advent of high-performance computing, we are now capable of simulating the ocean and climate system on decadal to centennial timescales. However, global and basin-scale simulations still lack the spatial resolution necessary to resolve the mesoscales (hereon referred to as mesoscale-permitting simulations), a scale roughly on the order of O(100 km). Here, we provide a first step towards a potential vorticity (PV) based mesoscale closure scheme in order to improve the representation of mesoscale eddies in such simulations by taking advantage of the thickness-weighted averaged (TWA) framework. In the TWA framework the total eddy feedback can be encapsulated in the Eliassen-Palm (E-P) flux divergence. This implies that mesoscale closure schemes aimed at representing the total eddy feedback should therefore be representing the E-P flux divergence. The TWA framework further elucidates that its divergence is equivalent to the eddy Ertel PV flux. In other words, if one is to parametrize the eddy Ertel PV flux, one has parametrized the total eddy feedback onto the mean flow. Using a 1/12° North Atlantic ensemble simulation with 24 members, which allows us to decompose the mesoscale variability from the forced dynamics, we show that the eddy Ertel PV flux can be related to the local-gradient of mean Ertel PV as an active tracer via an anisotropic eddy diffusivity tensor. What follows is that not only does the tensor bring together the isopycnal thickness skew diffusivity and isopycnic tracer diffusivity, the former known as the Gent-McWilliams (GM) parametrization and latter the Redi parametrization, but also incorporates the eddy momentum fluxes. Although the Redi parametrization has existed longer than GM, there has been much more development in the latter, leaving the Redi diffusivity poorly constrained. Being able to treat GM and Redi simultaneously is another strength of our framework.

The thickness-weighted average (TWA) framework, which treats the residual-mean flow as the prognostic variable, has provided us with a clear theoretical understanding of the eddy feedback onto the residual-mean flow. The averaging operator involved in the TWA framework, although in theory being an ensemble mean, in practice has often been approximated by a temporal mean, which conflates the temporal variability with the eddies. Here, we analyze an ensemble of North Atlantic simulations at mesoscale resolving resolution (1/12{degree sign}). We therefore recognize means and eddies in terms of ensemble means and fluctuations about those means, in keeping with the TWA formalism proposed by Young (2012). Eddy-mean flow feedbacks are encapsulated in the Eliassen-Palm (E-P) flux tensor and its divergence indicates that the eddies contribute to the zonal meandering of the Gulf Stream and its deceleration in the meridional direction. We also show that the eddy Ertel potential vorticity (PV) flux can be parametrized as an isopycnic local-gradient flux of the residual-mean Ertel PV via an anisotropic eddy diffusivity tensor. As the E-P flux divergence and eddy Ertel PV flux are directly related to one another, this provides a new pathway forward for a unified mesoscale eddy closure scheme.

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.

Mixing by mesoscale eddies in the ocean plays a major role in setting the distribution of oceanic tracers, with important implications for physical and biochemical systems at local to global scales. Roach et al. (2016; https://doi.org/10.1002/2015JC011440) demonstrated that a two‐particle analysis of Argo trajectories produces robust estimates of horizontal mixing in the Southern Ocean. Here we extend this analysis to produce global 1° × 1° maps of eddy diffusivity at the nominal Argo parking depth of 1,000 m. We also applied this methodology to estimate surface eddy diffusivities from Global Drifter Program (GDP) surface drifters. The global mean eddy diffusivity was 543 ± 155 m2/s at 1,000 m and 2637 ± 311 m2/s at the surface, with elevated diffusivities in regions of enhanced eddy kinetic energy, such as western boundary currents and along the Antarctic Circumpolar Current. The eddy kinetic energy at the equator is high at both the surface and depth, but the eddy diffusivity is only enhanced near the surface. At depth the eddy diffusivity is strongly suppressed due to the presence of mean flow. We used our observational estimates to test the validity of an eddy diffusivity parameterization that accounts for mixing suppression in the presence of zonal mean flows. Our results indicated that this parameterization generally agrees with the directly observed eddy diffusivities in the midlatitude and high‐latitude oceans.

Stirring in the subsurface Southern Ocean is examined using RAFOS float trajectories, collected during the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean (DIMES), along with particle trajectories from a regional eddy permitting model. A central question is the extent to which the stirring is local, by eddies comparable in size to the pair separation, or nonlocal, by eddies at larger scales. To test this, we examine metrics based on averaging in time and in space. The model particles exhibit nonlocal dispersion, as expected for a limited resolution numerical model that does not resolve flows at scales smaller than ~10 days or ~20–30 km. The different metrics are less consistent for the RAFOS floats; relative dispersion, kurtosis, and relative diffusivity suggest nonlocal dispersion as they are consistent with the model within error, while finite-size Lyapunov exponents (FSLE) suggests local dispersion. This occurs for two reasons: (i) limited sampling of the inertial length scales and a relatively small number of pairs hinder statistical robustness in time-based metrics, and (ii) some space-based metrics (FSLE, second-order structure functions), which do not average over wave motions and are reflective of the kinetic energy distribution, are probably unsuitable to infer dispersion characteristics if the flow field includes energetic wave motions that do not disperse particles. The relative diffusivity, which is also a space-based metric, allows averaging over waves to infer the dispersion characteristics. Hence, given the error characteristics of the metrics and data used here, the stirring in the DIMES region is likely to be nonlocal at scales of 5–100 km.

The primary productivity of the Southern Ocean ecosystem, and associated biological carbon pump, is limited by the availability of the micronutrient iron. Riverine sediments and atmospheric dust supply iron at the ocean margins, but in the vast open ocean, iron reaches phytoplankton primarily when iron-rich sub-surface waters enter the euphotic zone, linking vertical transport processes to ecosystem productivity. In addition to mixed-layer entrainment, recent studies in the North Atlantic and Southern Ocean suggest that eddy transport may be a highly effective pathway for nutrient transport. Here, high-resolution physical/biogeochemical simulations of an open-Southern-Ocean ecosystem forced with a realistic seasonal cycle reveal that primary production is sustained via iron supply across the mixed layer base primarily due to mesoscale and submesoscale turbulence (hereafter ``(sub)mesoscale eddies'). As model resolution is increased from 20 km to 5 km to 2 km, vertical eddy iron flux and phytoplankton biomass increase strongly, despite shoaling of the mixed layer. Diagnostics from eddy resolving runs show that the increase in primary production is supported by iron supply due to (sub)mesoscale isopycnal stirring. We also highlight that properly tuned eddy parametrizations in non-eddying runs can replicate this isopycnal flux and consequently the amount of biomass. One important consequence is that iron recycling is second-order importance in explaining sustained summertime productivity, as eddies continue to supply iron to the mixed layer throughout the year. Since eddy mixing rates are sensitive to wind forcing and large-scale hydrographic changes, these findings open a new mechanism for modulating the Southern Ocean biological pump on climate timescales.

In order to examine the roles of ocean dynamics in supplying iron, the limiting nutrient in the open Southern Ocean, to the surface where it can be effectively utilized for photosynthesis, we run a flat-bottom zonally re-entrant channel model configured to represent the Antarctic Circumpolar Current region and couple it to a full biogeochemical model. The model was forced with monthly varying physical and biogeochemical boundary conditions to incorporate seasonality. Much focus on previous studies on iron pathways in the open ocean region has been on mixed-layer entrainment and diapycnal fluxes of iron. The Southern Ocean, however, is a region with strong meso- and submeso-scale turbulence and we would expect eddy fluxes to transport tracers including iron. Spatial resolution is, therefore, chosen as the parameter to control the effect of eddy transport. We utilize cross spectral analysis and the generalized Omega equation to temporally and spatially decompose the vertical transport attributable to meso- and submeso-scale motions. Our results suggest that the mesoscale vertical fluxes provide a first-order pathway for transporting iron across the mixing-layer base where diapycnal mixing is weak and must be included in modelling the open-Southern-Ocean iron budget.

We provide the first observational estimate of the circumpolar distribution of cross‐stream eddy diffusivity at 1000 m in the Southern Ocean using Argo float trajectories. We show that Argo float trajectories, from the float surfacing positions, can be used to estimate lateral eddy diffusivities in the ocean and that these estimates are comparable to those obtained from RAFOS floats, where they overlap. Using the Southern Ocean State Estimate (SOSE) velocity fields to advect synthetic particles with imposed behavior that is "Argo‐like" and "RAFOS‐like" diffusivity estimates from both sets of synthetic particles agreed closely at the three dynamically very different test sites, the Kerguelen Island region, the Southeast Pacific Ocean, and the Scotia Sea, and support our approach. Observed cross‐stream diffusivities at 1000 m, calculated from Argo float trajectories, ranged between 300 and 2500 m2 s−1, with peaks corresponding to topographic features associated with the Scotia Sea, the Kerguelen Plateau, the Campbell Plateau, and the Southeast Pacific Ridge. These observational estimates agree with previous regional estimates from the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean (DIMES) near the Drake Passage, and other estimates from natural tracers (helium), inverse modeling studies, and current meter measurements. These estimates are also compared to the suppressed eddy diffusivity in the presence of mean flows. The comparison suggests that away from regions of strong topographic steering suppression explains both the structure and magnitude of eddy diffusivity but that eddy diffusivities in the regions of topographic steering are greater than what would be theoretically expected and the ACC experiences localized enhanced cross‐stream mixing in these regions.

The large-scale middepth circulation and eddy diffusivities in the southeast Pacific Ocean and Scotia Sea sectors between 110° and 45°W of the Antarctic Circumpolar Current (ACC) are described based on a subsurface quasi-isobaric RAFOS-float-based Lagrangian dataset. These RAFOS float data were collected during the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean (DIMES). The mean flow, adjusted to a common 1400-m depth, shows the presence of jets in the time-averaged sense with speeds of 6 cm s−1 in the southeast Pacific Ocean and upward of 13 cm s−1 in the Scotia Sea. These jets appear to be locked to topography in the Scotia Sea but, aside from negotiating a seamount chain, are mostly free of local topographic constraints in the southeast Pacific Ocean. The eddy kinetic energy (EKE) is higher than the mean kinetic energy everywhere in the sampled domain by about 50%. The magnitude of the EKE increases drastically (by a factor of 2 or more) as the current crosses over the Hero and Shackleton fracture zones into the Scotia Sea. The meridional isopycnal stirring shows lateral and vertical variations with local eddy diffusivities as high as 2800 ± 600 m2 s−1 at 700 m decreasing to 990 ± 200 m2 s−1 at 1800 m in the southeast Pacific Ocean. However, the cross-ACC diffusivity in the southeast Pacific Ocean is significantly lower, with values of 690 ± 150 and 1000 ± 200 m2 s−1 at shallow and deep levels, respectively, due to the action of jets. The cross-ACC diffusivity in the Scotia Sea is about 1200 ± 500 m2 s−1.

As part of the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean (DIMES), 210 subsurface floats were deployed west of the Drake Passage on two targeted density surfaces. Absolute (single particle) diffusivities are calculated for the floats. The focus is on the meridional component, which is less affected by the mean shear. The diffusivities are estimated in several ways, including a novel method based on the probability density function of the meridional displacements. This allows the determination of the range of possible lateral diffusivities, as well as the period over which the spreading can be said to be diffusive. The method is applied to the float data and to synthetic trajectories generated with the Massachusetts Institute of Technology General Circulation Model (MITgcm). Because of ballasting problems, many of the floats did not remain on their targeted density surface. However, the float temperature records suggest that most occupied a small range of densities, so the floats were grouped together for the analysis. The latter focuses on a subset of 109 of the floats, launched near 105°W. The different methods yield a consistent estimate for the diffusivity of 800 ± 200 m2 s−1. The same calculations were made with model particles deployed on 20 different density surfaces and the result for the particles deployed on the neutral density surface γ = 27.7 surface was the same within the errors. The model was then used to map the variation of the diffusivity in the vertical, near the core of the Antarctic Circumpolar Current (ACC). The results suggest mixing is intensified at middepths, between 1500 and 2000 m, consistent with several previous studies.