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Applying a variational analysis, a minimum-enstrophy vortex in three-dimensional (3-D) fluids with continuous stratification is found, under the quasi-geostrophic hypothesis. The buoyancy frequency is held constant. This vortex is an ideal limiting state in a flow with an enstrophy decay while energy and generalized angular momentum remain fixed. The variational method used to obtain two-dimensional (2-D) minimum-enstrophy vortices is applied here to 3-D integral quantities. The solution from the first-order variation is expanded on a basis of orthogonal spherical Bessel functions. By computing second-order variations, the solution is found to be a true minimum in enstrophy. This solution is weakly unstable when inserted in a numerical code of the quasi-geostrophic equations. After a stage of linear instability, nonlinear wave interaction leads to the reorganization of this vortex into a tripolar vortex. Further work will relate our solution with maximal entropy 3-D vortices.

Seasonal evolution of both surface signature and subsurface structure of a Mediterranean mesoscale anticyclones is assessed using the Coastal and Regional Ocean Community high‐resolution numerical model with realistic background stratification and fluxes. In good agreement with remote‐sensing and in‐situ observations, our numerical simulations capture the seasonal cycle of the anomalies induced by the anticyclone, both in the sea surface temperature (SST) and in the mixed layer depth (MLD). The eddy signature on the SST shifts from warm‐core in winter to cold‐core in summer, while the MLD deepens significantly in the core of the anticyclone in late winter. Our sensitivity analysis shows that the eddy SST anomaly can be accurately reproduced only if the vertical resolution is high enough (∼4 m in near surface) and if the atmospheric forcing contains high‐frequency. In summer with this configuration, the vertical mixing parameterized by the k − ϵ closure scheme is three times higher inside the eddy than outside the eddy, and leads to an anticyclonic cold core SST anomaly. This differential mixing is explained by near‐inertial waves, triggered by the high‐frequency atmospheric forcing. Near‐inertial waves propagate more energy inside the eddy because of the lower effective Coriolis parameter in the anticyclone core. On the other hand, eddy MLD anomaly appears more sensitive to horizontal resolution, and requires SST retroaction on air‐sea fluxes. These results detail the need of high frequency forcing, high vertical and horizontal resolutions to accurately reproduce the evolution of a mesoscale eddy. Plain Language Summary Mesoscale eddies are turbulent structures present in every regions of the world ocean, and accounting for a significant part of its kinetic energy budget. These structures can be tracked in time and recently revealed a seasonal cycle from in situ data. An anticyclone (clockwise rotating eddy in the northern hemisphere) is observed in the Mediterranean to be predominantly warm at the surface and to deepen the mixed layer in winter, but shifts to a cold‐core summer signature. This seasonal signal is not yet understood and studied in ocean models. In this study we assess the realism of an anticyclone seasonal evolution in high resolution numerical simulations. Eddy surface temperature seasonal shift is retrieved and is linked to an increased mixing at the eddy core spontaneously appearing at high vertical resolution (vertical grid size smaller than 4 m) in the presence of high frequency atmospheric forcing. This increased mixed is due to the preferred propagation of near‐inertial waves in the anticyclone due to its negative relative vorticity. Eddy‐induced mixed layer depth anomalies also appear to be triggered by sea surface temperature retroaction on air‐sea fluxes. These results suggest that present‐day operational ocean forecast models are too coarse to accurately retrieve mesoscale evolution. Key Points Enhanced mixing in anticyclones explain inverse eddy sea surface temperature (SST) signature Vertical resolution is crucial to model eddy core mixing triggered by near‐inertial waves Mixed layer anomaly is mainly driven by SST retroaction on air‐sea fluxes

Internal solitary waves (ISWs) propagate in stratified waters, enhancing diapycnal mixing, sediment and mass transport on shelves. They have typical wavelengths of hundreds of meters and tens of minutes periods, requiring high resolution and high frequency measurements for their sampling. But such in-situ measurements are scarce and ISWs remain largely unpredictable. We evidence that large amplitude ISWs propagating in the Strait of Gibraltar have a signature in the sea level at the Tarifa tide gauge and we propose an algorithm to automatically detect them. We validate the algorithm with in-situ measurements and satellite Sentinel-1 images. Thanks to the accuracy of this method, we analyse the ISW emission in the SoG from 2015 to 2023 from tidal to seasonal scales. This promising new method of in-situ ISW measurements offers potential benefits by supplying data on ISWs at various locations. These data will enhance our understanding of ISW dynamics, their parameterization and prediction.

The stability of a circular vortex is studied in the thermal quasi-geostrophic (TQG) model. Several radial distributions of vorticity and buoyancy (temperature) are considered for the mean flow. First, the linear stability of these vortices is addressed. The linear problem is solved exactly for a simple flow, and two stability criteria are then derived for general mean flows. Then, the growth rate and most unstable wavenumbers of normal-mode perturbations are computed numerically for Gaussian and cubic exponential vortices, both for elliptical and higher mode perturbations. In TQG, contrary to usual QG, short waves can be linearly unstable on shallow vorticity profiles. Linearly, both stratification and bottom topography (under specific conditions) have a stabilizing role. In a second step, we use a numerical model of the nonlinear TQG equations. With a Gaussian vortex, we show the growth of small-scale perturbations during the vortex instability, as predicted by the linear analysis. In particular, for an unstable vortex with an elliptical perturbation, the final tripolar vortices can have a turbulent peripheral structure, when the ratio of mean buoyancy to mean velocity is large enough. The frontogenetic tendency indicates how small-scale features detach from the vortex core towards its periphery, and thus feed the turbulent peripheral vorticity. We confirm that stratification and topography have a stabilizing influence as shown by the linear theory. Then, by varying the vortex and perturbation characteristics, we classify the various possible nonlinear regimes. The numerical simulations show that the influence of the growing small-scale perturbations is to weaken the peripheral vortices formed by the instability, and by this, to stabilize the whole vortex. A finite radius of deformation and/or bottom topography also stabilize the vortex as predicted by linear theory. An extension of this work to stratified flows is finally recommended.

This paper aims to analyze the North Brazil Current (NBC) rings during the initial 5 months of 2020 using surface currents derived from Automatic Identification System (AIS) data in comparison with altimetry-based Archiving, Validation and Interpretation of Satellite Oceanographic Data (AVISO) current fields. The region of NBC rings is characterized by relatively high marine traffic, facilitating an accurate current estimation. Our investigation primarily focused on a brief period coinciding with intensive in situ measurements (EUREC4A-OA experiment). The Angular Momentum Eddy Detection and tracking Algorithm (AMEDA) detection algorithm was then employed to detect and track eddies in both fields. Subsequently, a particular NBC ring present in the region in January and February 2020 was examined. The comparison demonstrated that AIS data exhibited the precision and resolution necessary to effectively identify the NBC rings and smaller surrounding eddies, aligning well with other datasets such as in situ measurements, sea surface temperature (SST), and sea surface salinity (SSS) data. Moreover, we established that AIS data yielded accurate regional velocity fields, as evidenced by an analysis of energy spectra. Furthermore, our analysis revealed that AIS data captured aspects of eddy–eddy interactions which were not adequately depicted in AVISO fields.

The instability of circular vortices is studied numerically in the surface quasigeostrophic (SQG) model, and their evolutions are compared with those of barotropically unstable 2D vortices. The growth rates in the SQG model evidence similarity with their barotropic counterparts for moderate radial gradients of temperature (or of vorticity in the 2D model). For stronger gradients, SQG vortices are more unstable than 2D vortices. The nonlinear, finite-amplitude evolutions of perturbed vortices provide evidence that moderately unstable, elliptically perturbed vortices form tripoles. When they are more unstable, they break into two dipoles. Weakly unstable vortices with triangular perturbations form transient quadrupoles that break; they stabilize only for large gradients of mean temperature. Finally, with square perturbations, pentapoles degenerate into dipoles, at least for the range of mean temperature gradients explored here. The analysis of nonlinear stabilizations reveals that the deformation of the vortex core and the leak of its temperature anomaly to the periphery are essential ingredients to stabilize the perturbation at finite amplitude. In conclusion, SQG vortex instability exhibits considerable similarity to the barotropic instability of 2D vortices.

North Brazil Current (NBC) rings are believed to play a key role in the Atlantic Ocean circulation and climate. Here, we use a new collection of high-resolution in-situ observations acquired during the EUREC4A-OA field experiment together with satellite altimetry to define, with unprecedented detail, the structure and evolution of these eddies. In-situ observations reveal a more complex structure than previously documented. In particular, we highlight a measurable impact of the Amazon outflow in creating a barrier layer over a large portion of the eddies. We show that this unprecedented data set allows us to estimate the accuracy of satellite altimetry gridded fields. The geostrophic velocities derived from satellite altimetry turn out to be considerably lower (up to 50% in amplitude) than the values measured by current meters. However, eddy properties as detected by TOEddies, a newly developed algorithm show to be relatively precise. For example, the eddy center and maximum azimuthal velocity contour fall within 25 ± 5 km and 16 ± 9 km, respectively, from the in-situ observed values. We apply TOEddies to 27 years of satellite altimetry to investigate the generic NBC rings behavior. We found a mean generation rate of 4.5 ± 1.1 rings per year, and a strong seasonal cycle in all eddy properties.

The Marquesas islands are a place of strong phytoplanktonic enhancement, whose original mechanisms have not been explained yet. Several mechanisms such as current−bathymetry interactions or island run-off can fertilize waters in the immediate vicinity or downstream of the islands, allowing phytoplankton enhancement. Here, we took the opportunity of an oceanographic cruise carried out at the end of 2018, to combine in situ and satellite observations to investigate two phytoplanktonic blooms occurring north and south of the archipelago. First, Lagrangian diagnostics show that both chlorophyll-a concentrations (Chl) plumes are advected from the islands. Second, the use of Finite-size Lyaponov Exponent and frontogenesis diagnostics reveal how the Chl plumes are shaped by the passage of a mesoscale cyclonic eddy in the south and by a converging front and finer-scale dynamic activity in the north. Our results based on these observations provide clues to the hypothesis of a fertilization from the islands themselves allowing phytoplankton to thrive. They also highlight the role of advection to disperse and shape the Chl plumes in two regions with contrasting dynamical regimes.

The theory of point vortices is used to explain the interaction of a surface vortex with subsurface vortices in the framework of a three-layer quasigeostrophic model. Theory and numerical experiments are used to calculate the interaction between one surface and one subsurface vortex. Then, the configuration with one surface vortex and two subsurface vortices of equal and opposite vorticities (a subsurface vortex dipole) is considered. Numerical experiments show that the self-propelling dipole can either be captured by the surface vortex, move in its vicinity, or finally be completely ejected on an unbounded trajectory. Asymmetric dipoles make loop-like motions and remain in the vicinity of the surface vortex. This model can help interpret the motions of Lagrangian floats at various depths in the ocean.

Deformation flows are the flows incorporating shear, strain and rotational components. These flows are ubiquitous in the geophysical flows, such as the ocean and atmosphere. They appear near almost any salience, such as isolated coherent structures (vortices and jets) and various fixed obstacles (submerged obstacles and continental boundaries). Fluid structures subject to such deformation flows may exhibit drastic changes in motion. In this review paper, we focus on the motion of a small number of coherent vortices embedded in deformation flows. Problems involving isolated one and two vortices are addressed. When considering a single-vortex problem, the main focus is on the evolution of the vortex boundary and its influence on the passive scalar motion. Two vortex problems are addressed with the use of point vortex models, and the resulting stirring patterns of neighbouring scalars are studied by a combination of numerical and analytical methods from the dynamical system theory. Many dynamical effects are reviewed with emphasis on the emergence of chaotic motion of the vortex phase trajectories and the scalars in their immediate vicinity.