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An ensemble of eddy-rich North Atlantic simulations is analyzed, providing estimates of kinetic energy wavenumber spectra and spectral budgets below the mixed layer where energy input from surface convection is negligible. A wavelet transform technique is used to estimate a localized `pseudo-Fourier' spectrum, permitting comparisons to be made between spectra at different locations in a highly inhomogeneous and anisotropic environment. We find evidence of a Gulf Stream imprint on the near Gulf Stream eddy field appearing as enhanced levels of kinetic energy (KE) in the North-South direction relative to the East-West direction. Surprisingly, this signature of anisotropy holds into the quiescent interior. We detect forward cascades of KE and enstrophy but find no clear evidence of upscale energy cascades in the separated Gulf Stream region, although an inverse cascade of KE emerges downstream of the separated Gulf Stream. The spectral slopes inferred from our analysis are significantly steeper than expected from quasi-geostrophic (QG) theory, but roughly in line with a primitive equation extension of the enstrophy inertial-range theory. A summary conclusion is that expectations regarding spectral slopes built on quasi-geostrophy are at best only weakly supported in primitive equations below the mixed layer where submesoscale dynamics are expected to be weak.

A wavelet-based method is re-introduced in an oceanographic and spectral context to estimate wavenumber spectrum and spectral flux of kinetic energy and enstrophy. We apply this to a numerical simulation of idealized, doubly-periodic quasi-geostrophic flows, i.e.~the flow is constrained by the Coriolis force and vertical stratification. The double periodicity allows for a straightforward Fourier analysis as the baseline method. Our wavelet spectra agree well with the canonical Fourier approach but with the additional strengths of negating the necessity for the data to be periodic and being able to extract local anisotropies in the flow. Caution is warranted, however, when computing higher-order quantities, such as spectral flux.

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?

With an increase in computational power, ocean models with kilometer-scale resolution have emerged over the last decade. Using these realistic simulations, we have been able to quantify the energetic exchanges between spatial scales and inform the design of eddy parametrizations. The increase in resolution, however, has drastically increased model outputs, making it difficult to transfer and analyze the data. The realism of individual models in representing the energetics down to numerical dissipation has also come into question. Here, we showcase a cloud-based analysis framework proposed by the Pangeo Project that aims to tackle such distribution and analysis challenges. We analyze seven submesoscale permitting simulations all on the cloud at a crossover region of the upcoming SWOT altimeter mission near the Gulf Stream separation. The models used in this study are based on the NEMO, CROCO, MITgcm, HYCOM, FESOM and FIO-COM code bases. The cloud-based analysis framework: i) minimizes the cost of duplicating and storing ghost copies of data, and ii) allows for seamless sharing of analysis results amongst collaborators. In this poster, we will describe the framework and provide preliminary results (e.g. spectra, vertical buoyancy flux, and how it compares to predictions from the mixed-layer instability parametrization). Basin-to-global scale, submesoscale-permitting models are still at their early stage of development ; their cost and carbon footprints are also rather large. It would, therefore, benefit the community to compile the different model configurations for future best practices. We also believe that an emphasis on data analysis strategies would be crucial for improving the models themselves.

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An ensemble of North Atlantic simulations is analyzed, providing estimates of kinetic energy spectra. A wavelet transform technique is used permitting comparisons to be made between spectra at different locations in this highly inhomogeneous environment. We find a strong tendency towards anisotropy in the spectra, with meridional spectra typically stronger than zonal spectra. This holds even in the gyre interior where conditions might be expected to be homogeneous. The spectra show reasonable ranges consistent with a downscale enstrophy cascade, but also a persistent tendency to exhibit steeper slopes at smaller scales. The only location where the presence of an upscale cascade is supported is the Gulf Stream extension. This is amongst first attempts to quantify and compare spectra and their differences in the inhomogeneous setting of the North Atlantic.

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.

With the increase in computational power, ocean models with kilometer-scale resolution have emerged over the last decade. These models have been used for quantifying the energetic exchanges between spatial scales, informing the design of eddy parametrizations and preparing observing networks. The increase in resolution, however, has drastically increased the size of model outputs, making it difficult to transfer and analyze the data. Nonetheless, it is of primary importance to assess more systematically the realism of these models. Here, we showcase a cloud-based analysis framework proposed by the Pangeo Project that aims to tackle such distribution and analysis challenges. We analyze the output of eight submesoscale-permitting simulations, all on the cloud, for a crossover region of the upcoming Surface Water and Ocean Topography (SWOT) altimeter mission near the Gulf Stream separation. The models used in this study are run with the NEMO, CROCO, MITgcm, HYCOM, FESOM and FIO-COM code bases. The cloud-based analysis framework: i) minimizes the cost of duplicating and storing ghost copies of data, and ii) allows for seamless sharing of analysis results amongst collaborators. We describe the framework and provide example analyses (e.g., sea-surface height variability, submesoscale vertical buoyancy fluxes, and comparison to predictions from the mixed-layer instability parametrization). Basin-to-global scale, submesoscale-permitting models are still at their early stage of development; their cost and carbon footprints are also rather large. It would, therefore, benefit the community to document the different model configurations for future best practices. We also argue that an emphasis on data analysis strategies would be crucial for improving the models themselves.

Understanding how kinetic energy (KE) is exchanged across scales and eventually dissipated remains a key question in physical oceanography. Recent theoretical works suggests that both quasi-balanced submesoscale motions and internal gravity waves (IGWs) could play a role in fluxing KE towards dissipation. How these classes of motions actually provide a route to dissipation in the ocean is still debated. This study investigates the impact of IGWs generated by tidal motions on cross-scale KE exchanges at mid-latitude. Our analysis is based on the output of two realistic submesoscale permitting ocean model simulations of the North Atlantic Ocean, run respectively with and without tidal forcing. These twin experiments permit investigation of how tidally-forced IGWs modify the KE variance, cross-scale exchanges, and associated seasonality. Our results show that, in the presence of externally-forced IGWs, KE transfer towards dissipative scales is enhanced in summertime both at the surface and in the ocean interior.

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 ...

Mesoscale eddies, the weather system of the oceans, although being on the scales of O(20-100km), have a disproportionate role in shaping the mean jets such as the separated Gulf Stream in the North Atlantic Ocean, which is on the scale of O(1000km) in the along-jet direction. With the increase in computational power, we are now able to partially resolve the eddies in basin-scale and global ocean simulations, a model resolution often referred to as mesoscale permitting. It is well known, however, that due to grid-scale numerical viscosity, mesoscale permitting simulations have less energetic eddies and consequently weaker eddy feedback onto the mean flow. In this study, we run a quasi-geostrophic model at mesoscale resolving resolution in a double gyre configuration and formulate a deterministic parametrization for the eddy rectification term of potential vorticity (PV), namely, the eddy PV flux divergence. We have moderate success in reproducing the spatial patterns and magnitude of eddy kinetic and potential energy diagnosed from the model. One novel point about our approach is that we account for non-local eddy feedbacks onto the mean flow by solving the eddy PV equation prognostically in addition to the mean flow. In return, we are able to parametrize the variability in total (mean+eddy) PV at each time step instead of solely the mean PV. A closure for the total PV is beneficial as we are able to account for both the mean state and extreme events.

The flow of energy in the wind‐driven circulation is examined in a combined theoretical and numerical study. Based on a multiple‐scale analysis, we find the mesoscale field in the ocean interior is strongly affected by, but does not feed back onto, the ventilated thermocline. In the western boundary region, the associated currents first appear as coastal jets, conserving mean energy, and later as separated jet extensions where the mesoscale is energized by the mean field. It is in the separated jet zone where the primary loss of general circulation energy to the mesoscale occurs. These ideas are tested by an analysis of a regional 1/12° primitive equation numerical model of the North Atlantic. The predictions of the theory are generally supported by the numerical results. The one exception is that topographic irregularities in the coastal jet spawn eddies, although these eddies contribute modestly to the energy budget. We therefore conclude the primary sink of wind input into the mean circulation is in the separated jet, and not the interior. The analysis also shows wind energy input to be much smaller than the interior energy fluxes; thus, the general circulation largely recirculates energy.

The `eddying' ocean, recognized for several decades, has been the focus of much observational and theoretical research. We here describe a generalization for the analysis of eddy energy, based in the use of ensembles, that addresses two key related issues: the definition of an `eddy' and the general computation of energy spectra. An ensemble identifies eddies as the unpredictable component of the flow, and permits the scale decomposition of their energy in inhomogeneous and non-stationary settings. It also avoids the `tapering' or `windowing' of the data required by traditional approaches. We apply the analysis to a mesoscale resolving (1/12 degree) ensemble of the separated North Atlantic Gulf Stream. Our results show that the eddies are consistent with the theoretical predictions of quasi-geostrophy both at the surface and ocean interior.

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.

In the upper ocean, submesoscale turbulence shows seasonal variability and is pronounced in winter. We analyze geostrophic KE spectra in a submesoscale-permitting global ocean model to study the seasonal variability in the upper ocean turbulence. Submesoscale processes peak in winter and, consequently, geostrophic kinetic energy (KE) spectra tend to be relatively shallow in winter (k-2) with steeper spectra in summer (k-3). The roles of frontogenesis processes and mixed-layer instabilities in submesoscale turbulence and their effects on the evolution of KE spectra over an annual cycle are discussed. It is shown that this transition in KE spectral scaling has two phases. In the first phase (late autumn), KE spectra show a presence of two spectral regimes: k-3 scaling in mesoscales (100-300 km) and k-2 scaling in submesoscales (< 50 km), indicating the coexistence of QG, surface-QG, and frontal dynamics. In the second phase (late winter), mixed-layer instabilities convert available potential energy into KE, which cascades upscale leading to flattening of the KE spectra at larger scales, and k-2 power-law develops in mesoscales too.

We examine the seasonal cycle of upper-ocean mesoscale turbulence in a high resolution CESM climate simulation. The ocean model component (POP) has 0.1° resolution, mesoscale resolving at low and middle latitudes. Seasonally and regionally resolved wavenumber power spectra are calculated for sea-surface eddy kinetic energy (EKE). Although the interpretation of the spectral slopes in terms of turbulence theory is complicated by the strong presence of dissipation and the narrow inertial range, the EKE spectra consistently show higher power at small scales during winter throughout the ocean. Potential hypotheses for this seasonality are investigated. Diagnostics of baroclinc energy conversion rates and evidence from linear quasigeostrophic stability analysis indicate that seasonally varying mixed-layer instability is responsible for the seasonality in EKE. The ability of this climate model, which is not considered submesoscale resolving, to produce mixed layer instability although damped by dissipation, demonstrates the ubiquity and robustness of this process for modulating upper ocean EKE.

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.

The application of a low-valent titanium reagent recently developed in our group, Ti(O-i-Pr)4/Me3SiCl/Mg, to the McMurry coupling polymerization of aryl dialdehyde monomers and [2 + 2 + 2] cycloaddition polymerization of aromatic diyne monomers is described. Furthermore, on the basis of these reactions, a low-valent titanium-mediated dual-mode coupling copolymerization of aryl dialdehyde and alkynylaldehyde monomers via concurrent McMurry olefination and alkyne cyclotrimerization reactions is proposed.