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  <front>
    <journal-meta><journal-id journal-id-type="publisher">OS</journal-id><journal-title-group>
    <journal-title>Ocean Science</journal-title>
    <abbrev-journal-title abbrev-type="publisher">OS</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Ocean Sci.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1812-0792</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/os-21-1933-2025</article-id><title-group><article-title>Synoptic observation of a full mesoscale eddy lifetime  and its secondary instabilities in the Gulf of Mexico</article-title><alt-title>Synoptic observation of mesoscale eddy</alt-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes" rid="aff1">
          <name><surname>de Marez</surname><given-names>Charly</given-names></name>
          <email>charly@hi.is</email>
        </contrib>
        <aff id="aff1"><label>1</label><institution>University of Iceland, Institute of Earth Sciences, Reykjavík, Iceland</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Charly de Marez (charly@hi.is)</corresp></author-notes><pub-date><day>4</day><month>September</month><year>2025</year></pub-date>
      
      <volume>21</volume>
      <issue>5</issue>
      <fpage>1933</fpage><lpage>1942</lpage>
      <history>
        <date date-type="received"><day>3</day><month>April</month><year>2025</year></date>
           <date date-type="rev-request"><day>10</day><month>April</month><year>2025</year></date>
           <date date-type="rev-recd"><day>23</day><month>June</month><year>2025</year></date>
           <date date-type="accepted"><day>27</day><month>June</month><year>2025</year></date>
      </history>
      <permissions>
        <copyright-statement>Copyright: © 2025 Charly de Marez</copyright-statement>
        <copyright-year>2025</copyright-year>
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://os.copernicus.org/articles/21/1933/2025/os-21-1933-2025.html">This article is available from https://os.copernicus.org/articles/21/1933/2025/os-21-1933-2025.html</self-uri><self-uri xlink:href="https://os.copernicus.org/articles/21/1933/2025/os-21-1933-2025.pdf">The full text article is available as a PDF file from https://os.copernicus.org/articles/21/1933/2025/os-21-1933-2025.pdf</self-uri>
      <abstract><title>Abstract</title>

      <p id="d2e80">Mesoscale eddies are crucial to ocean circulation, climate, and tracer transport. Yet their life cycle has never been observed synoptically at high resolution. In this study, I use novel SWOT satellite altimetry data to present the first synoptic characterization of a loop current eddy's life cycle in the Gulf of Mexico, during a 6-month period. SWOT allows for the direct observation of key dynamical processes – such as eddy shielding, high-mode instabilities, and dipolar interactions – that were previously only partially resolved in interpolated altimetry products and mainly described in theoretical or numerical studies. These observations challenge the traditional view of eddies as simple, elliptical structures, emphasizing the role of mesoscale interactions in their evolution. Furthermore, SWOT captures intense submesoscale turbulence at the eddy's rim, revealing secondary instabilities likely driving its decay. These findings not only validate decades of vortex theory but also offer new insights into oceanic turbulence dynamics.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <label>1</label><title>Introduction</title>
      <p id="d2e92">The study of oceanic vortices, or eddies, has been a cornerstone of oceanography for decades, driven by the critical role these features play in biological activities <xref ref-type="bibr" rid="bib1.bibx12" id="paren.1"/>, tracer transport <xref ref-type="bibr" rid="bib1.bibx66" id="paren.2"/>, and properties of the water column <xref ref-type="bibr" rid="bib1.bibx23" id="paren.3"/>. In particular, the mesoscale (10–100 km) eddy field is at least as energetic as the large-scale circulation <xref ref-type="bibr" rid="bib1.bibx66" id="paren.4"/>, essential for the air–sea interactions <xref ref-type="bibr" rid="bib1.bibx56" id="paren.5"/> and thus for the evolution of climate <xref ref-type="bibr" rid="bib1.bibx50" id="paren.6"/>. Early observations of oceanic mesoscale eddies were limited by the resolution of available data, primarily relying on ship-based measurements, which provided isolated snapshots of ocean conditions <xref ref-type="bibr" rid="bib1.bibx25" id="paren.7"/>. With the advent of satellite measurements in the late 20th century – first with sea surface temperature (SST) radiometry <xref ref-type="bibr" rid="bib1.bibx53" id="paren.8"/>, then altimetric sea surface height (SSH) <xref ref-type="bibr" rid="bib1.bibx10" id="paren.9"/> – the tracking of mesoscale eddy surface signatures improved dramatically. This enabled global-scale analyses <xref ref-type="bibr" rid="bib1.bibx11" id="paren.10"/>, though at low resolution (typically <inline-formula><mml:math id="M1" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:math></inline-formula>°). In parallel, the theoretical and numerical understanding of mesoscale eddy dynamics has advanced significantly, offering valuable insights into eddy behavior through fluid mechanics <xref ref-type="bibr" rid="bib1.bibx41" id="paren.11"><named-content content-type="pre">see the literature of vortex studies since</named-content></xref>. However, the inability to synoptically measure the horizontal structure of eddies at high resolution – particularly dynamic quantities – during their lifetime remains a significant observational gap, hindering the global validation of these theoretical and numerical studies.</p>
      <p id="d2e144">In the ocean, mesoscale eddies form a complex “soup” of currents, yet some eddies exhibit distinct patterns – such as a large diameter, recurrence, long lifetimes, and isolation – that make them ideal candidates for studying their specific dynamics in greater detail. The most famous examples lie in the western boundaries of oceanic basins: the Gulf Stream rings <xref ref-type="bibr" rid="bib1.bibx52" id="paren.12"/>, the Agulhas rings <xref ref-type="bibr" rid="bib1.bibx49" id="paren.13"/>, the Kuroshio rings <xref ref-type="bibr" rid="bib1.bibx37" id="paren.14"/>, or the loop current eddies <xref ref-type="bibr" rid="bib1.bibx42" id="paren.15"><named-content content-type="pre">LCEs;</named-content></xref>. The latter are large, recurrent features in the Gulf of Mexico, whose evolution has been extensively studied both numerically and observationally since decades <xref ref-type="bibr" rid="bib1.bibx30" id="paren.16"/>. LCEs form at the boundary of the loop current, stirring the surrounding water masses as they drift, shaping the hydrography of the Gulf of Mexico <xref ref-type="bibr" rid="bib1.bibx55" id="paren.17"/>. LCEs have been shown to impact pollutant transport <xref ref-type="bibr" rid="bib1.bibx28" id="paren.18"><named-content content-type="pre">see, e.g.,</named-content></xref>. They are also key for heat transport, thus creating strong air–sea exchanges, particularly important in this area for hurricane intensification <xref ref-type="bibr" rid="bib1.bibx54" id="paren.19"/>.</p>
      <p id="d2e176">The ability to track the dynamics of eddies such as LCEs has been made possible through gridded altimetry, which allows for the detection of their spatial extent and evolution over time <xref ref-type="bibr" rid="bib1.bibx39" id="paren.20"/>. Despite its usefulness in recovering some of the eddies' dynamical properties (e.g., radius, velocity, amplitude), this approach has large flaws, mainly due to the fact that the spatiotemporal interpolation often fails to provide full confidence in accurately capturing the horizontal shape of oceanic features <xref ref-type="bibr" rid="bib1.bibx35" id="paren.21"/> from their birth until their death.</p>
      <p id="d2e185">The Surface Water and Ocean Topography <xref ref-type="bibr" rid="bib1.bibx47" id="paren.22"><named-content content-type="pre">SWOT;</named-content></xref> program, a collaborative effort between CNES and NASA launched in late 2022, marks a pivotal advancement in the measure of mesoscale eddies in the ocean. With its unprecedented spatial resolution and 2D instantaneous coverage, SWOT enables synoptic observation of ocean features with fine-scale precision. In this study, I demonstrate the ability of SWOT to capture the evolution of a mesoscale eddy, focusing on a loop current eddy in the Gulf of Mexico. This highlights the capacity of modern altimetry to bridge the gap between numerical predictions and real-time observations of oceanic vortices.</p>
</sec>
<sec id="Ch1.S2">
  <label>2</label><title>Synoptical description of the full loop current eddy life cycle</title>
      <p id="d2e201">SWOT's non-interpolated swaths (see full details in Appendix <xref ref-type="sec" rid="App1.Ch1.S1"/>) provide continuous, high-resolution observations of a particular LCE's horizontal structure during its lifetime (Fig. <xref ref-type="fig" rid="F1"/>a–r), between its formation in early October 2023 until the end of March 2024.</p>

      <fig id="F1" specific-use="star"><label>Figure 1</label><caption><p id="d2e210">Evolution of the loop current eddy (LCE) over its lifetime from 2 km resolution SWOT altimetry. Each panel shows the <inline-formula><mml:math id="M2" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:math></inline-formula>° gridded AVISO sea level anomaly (SLA) as the background color for the indicated date; note that the color mapping of AVISO SLA is voluntarily paler for presentation purpose. Superimposed are the 2 km denoised SWOT SLA measurements along passes within <inline-formula><mml:math id="M3" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">3.5</mml:mn></mml:mrow></mml:math></inline-formula> d of the given date. The black contour marks the LCE detection from gridded altimetry, while thin gray contours represent iso-SLA lines from SWOT passes at 5 cm intervals. All panels have the same <inline-formula><mml:math id="M4" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula>- and <inline-formula><mml:math id="M5" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula>-axis ranges. The labels LCE<sub>0</sub>, LCT<sub>0</sub>, LCE, VS, C<sub>1</sub>, C<sub>2</sub>, C<sub>3</sub>, C<sub>4</sub>, and LCT<sub>1</sub> will be discussed in the main text.</p></caption>
        <graphic xlink:href="https://os.copernicus.org/articles/21/1933/2025/os-21-1933-2025-f01.jpg"/>

      </fig>

      <p id="d2e319">In August 2023, a pre-existing large anticyclone (LCE<sub>0</sub>) was positioned near 27° N, 90° W. Around the same time, the loop current overshot into the Gulf of Mexico, forming a loop current tongue (LCT<sub>0</sub>, also referred to in the literature as an “extended mode loop current”). The latter subsequently merged with LCE<sub>0</sub> (Fig. <xref ref-type="fig" rid="F1"/>a–d), absorbing it in what has been referred to as a “reattachment” sequence, a process previously identified in regional numerical modeling studies of the Gulf of Mexico <xref ref-type="bibr" rid="bib1.bibx48" id="paren.23"/> and gridded altimetry <xref ref-type="bibr" rid="bib1.bibx38" id="paren.24"/>. In early October, the loop current detached, generating the LCE that is the focus of this study. This newly formed eddy was then trapped within a train of alternating-polarity eddies, with opposite-signed sea level anomalies (SLAs) emerging to both its west and east (Fig. <xref ref-type="fig" rid="F1"/>d–f). As it stirred surrounding vortices of opposite polarities – marked by negative SLA patches – it created a strong vorticity shield (VS), i.e., a ring of opposite-sign (cyclonic) vorticity surrounding the eddy <xref ref-type="bibr" rid="bib1.bibx60" id="paren.25"/>. By early December, the LCE had settled into a nearly circular shape, its VS effectively <italic>isolating</italic> it from external influences (Fig. <xref ref-type="fig" rid="F1"/>g).</p>
      <p id="d2e369">In December 2023, the LCE undergoes a <italic>destabilization</italic> sequence. Its VS transitions into a rotating train of four cyclones (C<sub>1–4</sub>; see Fig. <xref ref-type="fig" rid="F1"/>h–m). While the companion cyclones may not all be generated de novo by the instability, their coherent configuration and evolution suggest that the LCE instability reinforces a dominant mode-4 structure. This kind of structure has been referred to by various names in past studies, including “squared vortex”, “pentapole”, and “mode-4 vortex”. It has long been predicted by numerical simulations and theoretical studies <xref ref-type="bibr" rid="bib1.bibx46 bib1.bibx14" id="paren.26"><named-content content-type="pre">see, e.g.,</named-content><named-content content-type="post">and our own simulations in Appendix <xref ref-type="sec" rid="App1.Ch1.S2"/></named-content></xref> and stands as a textbook example of eddy destabilization. Such vortical structures with intense satellite vortices are typically self-destructive <xref ref-type="bibr" rid="bib1.bibx9" id="paren.27"/>, and the mode-4 structure often leads to rapid eddy decay. Here, the LCE remains coherent, suggesting that external interactions, likely with surrounding mesoscale structures, modulate the instability and prevent the eddy’s destruction.</p>
      <p id="d2e402">In January 2024, a new loop current tongue (LCT<sub>1</sub>) forms as the loop current undergoes another detachment (Fig. <xref ref-type="fig" rid="F1"/>n). Unlike in August 2023, when LCT<sub>0</sub> merged with a pre-existing eddy (LCE<sub>0</sub>), this time, satellite cyclones C<sub>2,4</sub> act as a barrier: the presence of these vortices prevents the merging of LCT<sub>1</sub> with the LCE (Fig. <xref ref-type="fig" rid="F1"/>p). This directly confirms previous model- and altimetry-based predictions <xref ref-type="bibr" rid="bib1.bibx34" id="paren.28"/> of LCE shedding being blocked by cyclonic activity in the eastern Gulf of Mexico. Here, I further show that these cyclonic structures are generated by the LCE's own instabilities and play a major role in determining its fate. As the system evolves, two of the cyclonic satellites, C<sub>1</sub> and C<sub>2</sub>, are expelled eastward by LCT<sub>1</sub> (see black arrow in Fig. <xref ref-type="fig" rid="F1"/>o), leaving the LCE with only two remaining companions (Fig. <xref ref-type="fig" rid="F1"/>o–q). While SWOT does not provide full coverage of their trajectory, it is likely that C<sub>1</sub> and C<sub>2</sub> eventually merge. This sequence alters the symmetry of the system, leaving the LCE coupled with a single cyclone (C<sub>4</sub>). The result is the formation of a dipole (Fig. <xref ref-type="fig" rid="F1"/>q).</p>
      <p id="d2e524">In mid-February, the dipole begins to drift steadily westward (Fig. <xref ref-type="fig" rid="F1"/>q–s; the dipolar movement is schematized by the black arrow in Fig. <xref ref-type="fig" rid="F1"/>q), guiding the LCE toward the well-known <italic>eddy graveyard</italic> at the western boundary of the Gulf of Mexico <xref ref-type="bibr" rid="bib1.bibx3 bib1.bibx58" id="paren.29"/>. The dipole slightly deviates northward due to the asymmetry of the dipolar structure. As it moves, the LCE gradually loses energy and weakens, as seen by its loss in SLA amplitude and as previously demonstrated in <xref ref-type="bibr" rid="bib1.bibx44" id="text.30"/>. This westward drift is not primarily driven by planetary Rossby wave propagation, as traditionally assumed in the literature <xref ref-type="bibr" rid="bib1.bibx13 bib1.bibx20" id="paren.31"><named-content content-type="pre">see, e.g.,</named-content></xref>. In this particular case, the drift results from a dipolar interaction between the LCE and its remaining cyclone companion, which emerges during the instability phase. This highlights that, at least for the event studied here, mesoscale interactions can play a dominant role in shaping the trajectory of loop current eddies and suggests that stability properties and eddy–eddy interactions should be considered alongside large-scale wave dynamics.</p>
      <p id="d2e546">I was able to analyze the complete life cycle of a loop current eddy with unprecedented spatial detail. Previous studies relied on low-resolution, gridded altimetry products that required spatiotemporal interpolation and strong assumptions to reconstruct eddy evolution <xref ref-type="bibr" rid="bib1.bibx30" id="paren.32"><named-content content-type="pre">see, e.g.,</named-content></xref>, while high-resolution observations, such as sea surface temperature, provided only partial insights without direct velocity estimates <xref ref-type="bibr" rid="bib1.bibx29" id="paren.33"/>. This observational gap limited the ability to clearly identify key dynamical features – such the emergence of high-mode instabilities – which, in interpolated altimetric fields, can be smoothed or distorted and occasionally misrepresented <xref ref-type="bibr" rid="bib1.bibx35" id="paren.34"/>.</p>
      <p id="d2e560">More broadly, in the global ocean, classical altimetry studies primarily characterized eddy self-evolution through their <italic>ellipticity</italic>, a proxy for mode-2 deformations affecting velocity estimates <xref ref-type="bibr" rid="bib1.bibx33" id="paren.35"/>. However, they could not resolve more complex structures. With SWOT's high-resolution altimetry, as demonstrated here, I now observe higher-order modes, revealing that eddies are not merely elliptical but can exhibit much sharper gradients than previously thought. This challenges the long-standing view of eddies as circular structures and suggests that velocity estimates commonly used in global studies <xref ref-type="bibr" rid="bib1.bibx66" id="paren.36"/> may require revision using SWOT's high-resolution data.</p>
      <p id="d2e572">The present observation confirms that the mechanisms governing oceanic mesoscale eddy evolution – instability growth, eddy shielding, and dipolar interactions – are fully consistent with theoretical and numerical “vortex studies” dating back to the 1980s <xref ref-type="bibr" rid="bib1.bibx32 bib1.bibx26" id="paren.37"><named-content content-type="pre">e.g.,</named-content></xref>. However, unlike past descriptions that often treated these processes separately, I now see that these textbook mechanisms are not isolated processes; rather, they are deeply entangled, continuously interacting and shaping the oceanic mesoscale eddies evolution in complex ways.</p>
      <p id="d2e581">Being able to observe the horizontal shape of long-living eddies with such accuracy is particularly significant for the vortex dynamics community, which has long relied on numerical and theoretical predictions to study mesoscale eddies in the ocean. The lack of direct, high-resolution observations has remained a major limitation, leaving key aspects of vortex evolution unverified in real-ocean conditions. The present observations show evidence that the textbook mechanisms of vortex instability and decay are consistent with 4 decades of theoretical and numerical work. These results mark a turning point, opening new perspectives for both theoretical and modeling studies of oceanic eddies and their role in large-scale ocean circulation, as well as in helping the near-real-time monitoring and interpretation of the vertical structure of those eddies through, e.g., autonomous glider deployment <xref ref-type="bibr" rid="bib1.bibx42" id="paren.38"/>.</p>
</sec>
<sec id="Ch1.S3">
  <label>3</label><title>Observation of secondary instabilities at the rim of the eddy</title>
      <p id="d2e595">Beyond the mesoscale dynamics governing the LCE's evolution, a closer look at its periphery reveals the presence of intense submesoscale instabilities.</p>
      <p id="d2e598">Until now, the sharpness of eddy rims has been largely masked by low-resolution altimetric products. Here, the highest-resolution SWOT product (with a 250 m spacing grid) resolves the steep SLA gradients at the edge of the LCE. I present two particular times, where four distinct SWOT passes sampled the quasi-totality of the LCE's northern edge, one before its destabilization sequence early December (Fig. <xref ref-type="fig" rid="F2"/>a, c, and e), and another one after the mode-4 structure emerged (Fig. <xref ref-type="fig" rid="F2"/>b, d, and f). The latest SWOT data processing now provides direct velocity estimates at the eddy's edge, revealing remarkably fine-scale dynamics. Current magnitudes reach up to <inline-formula><mml:math id="M28" display="inline"><mml:mrow><mml:mi mathvariant="script">O</mml:mi><mml:mo>(</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> m s<sup>−1</sup>, with velocity variations over very short distances, resulting in sharp velocity gradients. These gradients are particularly enhanced between the satellite cyclone and the LCE core in January (Fig. <xref ref-type="fig" rid="F2"/>d), reinforcing the idea that the primary instability of the LCE further steepened these gradients. This confirms previous studies using numerical modeling discussing the velocity gradient sharpness at LCEs' edges <xref ref-type="bibr" rid="bib1.bibx31" id="paren.39"/>.</p>

      <fig id="F2" specific-use="star"><label>Figure 2</label><caption><p id="d2e639">Observation of secondary instabilities at the rim of the loop current eddy from 250 m resolution SWOT altimetry. <bold>(a, b)</bold> Same as Fig. <xref ref-type="fig" rid="F1"/>g and m but zoomed in and using the 250 m denoised SWOT SLA product. Black contour shown in all panels marks the LCE detection from gridded altimetry, while additional black contours in panels <bold>(a, b)</bold> indicate iso-SLA lines from SWOT passes at 2 cm intervals in the range <inline-formula><mml:math id="M30" display="inline"><mml:mrow><mml:mn mathvariant="normal">0</mml:mn><mml:mo>&lt;</mml:mo><mml:mi mathvariant="normal">SLA</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">0.2</mml:mn></mml:mrow></mml:math></inline-formula> m; note that the color map is the same as in Fig. <xref ref-type="fig" rid="F1"/>. <bold>(c, d)</bold> Geostrophic current magnitude derived from the denoised SWOT SLA. <bold>(e, f)</bold> Normalized relative vorticity computed from the geostrophic currents shown in <bold>(c, d)</bold>. In panels <bold>(c)</bold>–<bold>(f)</bold>, the same quantity derived from AVISO SLA is shown in the background, with a paler color mapping for presentation purposes.</p></caption>
        <graphic xlink:href="https://os.copernicus.org/articles/21/1933/2025/os-21-1933-2025-f02.jpg"/>

      </fig>

      <p id="d2e691">These conditions are well known to generate submesoscale features through various dynamical instabilities, including barotropic, baroclinic, and centrifugal instabilities <xref ref-type="bibr" rid="bib1.bibx40" id="paren.40"/>. Additionally, in the case of the LCE described here, a surface mixed layer is present (about 100 m deep, as seen in in situ data not shown here), favoring surface quasi-geostrophic (SQG) dynamics. This enhances the development of submesoscale structures <xref ref-type="bibr" rid="bib1.bibx7" id="paren.41"><named-content content-type="pre">see our SQG simulation reproducing the LCE conditions in Appendix <xref ref-type="sec" rid="App1.Ch1.S2"/> and, e.g.,</named-content></xref>. Here, I observe that the strong frontal gradients at the eddy’s rim trigger <italic>secondary instabilities</italic>, a process extensively described by <xref ref-type="bibr" rid="bib1.bibx19" id="text.42"/>. This leads to the formation of intense submesoscale coherent vortices (SCVs) and filaments with high vorticity values (<inline-formula><mml:math id="M31" display="inline"><mml:mrow><mml:mi mathvariant="italic">ζ</mml:mi><mml:mo>/</mml:mo><mml:mi>f</mml:mi><mml:mo>&gt;</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:math></inline-formula>), as clearly visible in Fig. <xref ref-type="fig" rid="F2"/>e and f.</p>
      <p id="d2e729">Numerical models have long predicted the formation of such fronts, filaments, and submesoscale coherent vortices at the edges of mesoscale eddies <xref ref-type="bibr" rid="bib1.bibx4" id="paren.43"><named-content content-type="pre">see for example Fig. 2 of</named-content></xref>. However, observational evidence of such structures has remained scarce. On the one hand, snapshots from high-resolution satellite imagery, such as chlorophyll-<inline-formula><mml:math id="M32" display="inline"><mml:mi>a</mml:mi></mml:math></inline-formula> concentration, have only hinted at their presence <xref ref-type="bibr" rid="bib1.bibx36" id="paren.44"/>. On the other hand, occasional in situ measurements have reported isolated snapshots of submesoscale processes at eddy peripheries <xref ref-type="bibr" rid="bib1.bibx43 bib1.bibx51" id="paren.45"><named-content content-type="pre">in particular in LCE cases using ocean gliders; see</named-content></xref>. Thus, without synoptic velocity fields, direct observations of these intense vorticity structures were lacking. This raised a fundamental question in numerical oceanography: were these submesoscale features real or merely numerical artifacts arising from ad hoc parameterizations? For the case of this LCE, SWOT provides an unambiguous observational answer. Applied to the global ocean, it will therefore likely reveal the ubiquity of intense submesoscale turbulence around eddies.</p>
      <p id="d2e752">Submesoscale secondary instabilities play a crucial role in the long-term decay of eddies, including the LCE observed in this study. These instabilities drive the gradual loss of energy and mass of eddies, as momentum and tracers are redistributed over shorter timescales than those associated with mesoscale processes alone. This mechanism provides a pathway for energy dissipation. Our observations align with previous in situ studies showing that LCEs steadily lose amplitude as they drift westward <xref ref-type="bibr" rid="bib1.bibx45" id="paren.46"/>. This has important implications for heat transport and air–sea interactions. Eddies like the LCE store and redistribute large amounts of heat during their lifetime <xref ref-type="bibr" rid="bib1.bibx44" id="paren.47"/>, but the mechanisms controlling their heat loss remain uncertain. Submesoscale processes likely enhance lateral heat release by increasing diffusivity at the eddy periphery <xref ref-type="bibr" rid="bib1.bibx27" id="paren.48"/>. Along with recent studies, this suggests that existing parameterizations of eddy-driven heat fluxes may need revision and update to account for submesoscale processes.</p>
</sec>
<sec id="Ch1.S4" sec-type="conclusions">
  <label>4</label><title>Conclusions</title>
      <p id="d2e772">This study marks a significant advance in satellite oceanography by providing the first synoptic, high-resolution observation of the full development and mature evolution of a mesoscale eddy, captured continuously over several months. It also illustrates that high-resolution satellite altimetry can resolve submesoscale instabilities at the edge of an eddy, providing new insights into the small-scale processes that contribute to eddy decay.</p>
      <p id="d2e775">While this represents a single case study, the implications are far-reaching. With SWOT's unprecedented resolution, the oceanographic community can now extend this approach globally, enabling a systematic characterization of mesoscale eddy life and submesoscale turbulence across all ocean basins. This is a crucial step toward closing the oceanic energy budget, bridging the gap between mesoscale eddy dynamics and smaller-scale dissipative processes. Unlike machine learning approaches, which often provide parameterizations without physical interpretability, SWOT will likely allow us to observe, analyze, and ultimately derive physics-based parameterizations of small-scale turbulence. This ensures a deeper understanding of ocean dynamics and paves the way for improved modeling of the Earth's complex systems.</p>
</sec>

      
      </body>
    <back><app-group>

<app id="App1.Ch1.S1">
  <label>Appendix A</label><title>SWOT altimetry</title>
      <p id="d2e790">I leverage newly released SWOT satellite data <xref ref-type="bibr" rid="bib1.bibx47" id="paren.49"><named-content content-type="pre">see some background in, e.g.,</named-content></xref>, and in particular, I use the latest release (v2.0.1) of Level-3 SWOT data, namely SWOT_L3_SSH “Basic” (2 km resolution) and “Unsmoothed” (250 m resolution) products, derived from the L3 SWOT KaRIn Low rate ocean data products provided by NASA/JPL and CNES. The Level-3 processing removes SWOT's systematic errors and has been extensively validated using other altimeters, numerical models, and in situ data in the global ocean <xref ref-type="bibr" rid="bib1.bibx21" id="paren.50"/>. These datasets are produced and freely distributed by the AVISO and DUACS teams as part of the DESMOS Science Team project <xref ref-type="bibr" rid="bib1.bibx1 bib1.bibx2" id="paren.51"/>. I use the “denoised” SLA for our analysis <xref ref-type="bibr" rid="bib1.bibx22" id="paren.52"><named-content content-type="pre">see</named-content><named-content content-type="post">for details on the method</named-content></xref>, as well as the geostrophic velocity derived from it. Note that this process tends to reduce the overall energy, which complicates the interpretation in lower-energy regions due to the noise levels <xref ref-type="bibr" rid="bib1.bibx5" id="paren.53"><named-content content-type="pre">see, e.g.,</named-content></xref>. This has no implication in our case, given the very high energy level of the LCE and its surroundings. However, note that this procedure may lead to spurious velocity patterns at the edge of swaths, thus leading to vorticity artifacts that should not be taken into account for the analysis. Recent studies <xref ref-type="bibr" rid="bib1.bibx65 bib1.bibx67 bib1.bibx61 bib1.bibx24 bib1.bibx17 bib1.bibx62 bib1.bibx57 bib1.bibx8 bib1.bibx21 bib1.bibx64" id="paren.54"/> and ongoing personal work show the SWOT's ability to resolve small mesoscale structures previously undetected in gridded products. Also, other recent studies have demonstrated that SWOT’s resolution and noise level are sufficient to resolve features at the submesoscale, particularly in regions of strong mesoscale activity. In particular, <xref ref-type="bibr" rid="bib1.bibx59" id="text.55"/>, <xref ref-type="bibr" rid="bib1.bibx15" id="text.56"/>, and <xref ref-type="bibr" rid="bib1.bibx63" id="text.57"/> provide detailed analyses of SWOT’s capability to capture fine-scale dynamics, including assessments of geostrophic vorticity derived from SLA fields. These works support the interpretation of small-scale structures such as those shown in Fig. <xref ref-type="fig" rid="F2"/>, even in high-Rossby-number regimes. I refer the reader to these studies for an in-depth evaluation of SWOT's performance in such contexts. Therefore, although a complete in situ validation is not yet available in our study area, I have no doubt that SWOT's resolution is able to capture the dynamics of the LCE and its surroundings.</p>

      <fig id="FA1"><label>Figure A1</label><caption><p id="d2e833">Eddy stability numerical simulations. <bold>(a–d)</bold> Snapshots of the upper-layer streamfunction from low-resolution two-layer quasi-geostrophic (QG) simulations, initialized with <inline-formula><mml:math id="M33" display="inline"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>=</mml:mo><mml:mo>[</mml:mo><mml:mn mathvariant="normal">2</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">3</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">4</mml:mn><mml:mo>,</mml:mo><mml:mn mathvariant="normal">5</mml:mn><mml:mo>]</mml:mo></mml:mrow></mml:math></inline-formula>. <bold>(e)</bold> Upper-layer vorticity snapshot from a high-resolution two-layer QG simulation, using the same parameters as in <bold>(d)</bold>; dashed and solid contours show <inline-formula><mml:math id="M34" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">0.05</mml:mn></mml:mrow></mml:math></inline-formula> and 0.1 streamfunction contours, respectively. <bold>(f)</bold> Surface vorticity snapshot from a high-resolution surface quasi-geostrophic (SQG) simulation, also using the same parameters as in <bold>(d)</bold>.</p></caption>
        <graphic xlink:href="https://os.copernicus.org/articles/21/1933/2025/os-21-1933-2025-f03.png"/>

      </fig>

      <p id="d2e896">To track the eddy's lifetime, I identified its center position each week using a gridded altimetric product (<inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>/</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:math></inline-formula>° AVISO SLA). Around this position, I selected the closest SWOT tracks sampled within <inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:mo>±</mml:mo><mml:mn mathvariant="normal">3.5</mml:mn></mml:mrow></mml:math></inline-formula> d of the detected eddy center date. For example, SWOT's passes in Fig. <xref ref-type="fig" rid="F1"/>g are from passes 175, 203, 244, and 272 of SWOT cycle 7, respectively sampled on 29, 30 November, and 2 and 3 December 2023. Since SWOT measurements are near-instantaneous compared to timescales of interest (e.g., weeks to months for eddy destabilization; see Fig. <xref ref-type="fig" rid="FA1"/>), this approach ensures spatiotemporal continuity. It also guarantees that, in each panel of Fig. <xref ref-type="fig" rid="F1"/>, time gaps between passes remain too small to affect our conclusions. This approach ensures, for example, (1) a full spatiotemporal coverage of the LCT<sub>0</sub> during the LCE formation (Fig. <xref ref-type="fig" rid="F1"/>a–d); (2) the fact that the small cyclones C<sub>1–4</sub> are LCE satellites and not part of another larger cyclones (Fig. <xref ref-type="fig" rid="F1"/>l); and (3) that the dipole in Fig. <xref ref-type="fig" rid="F1"/>o–r remains coherent over time, driving the westward drift of the LCE.</p>
</app>

<app id="App1.Ch1.S2">
  <label>Appendix B</label><title>Numerical modeling</title>
      <p id="d2e965">Using a simple numerical setup I reproduce some of the classical results found in earlier “vortex studies” that mirror our observations.</p>
      <p id="d2e968">First, I integrate a two-layer quasi-geostrophic (QG) model in order to observe the emergence of azimuthal modal structures from the destabilization of a LCE-like eddy. Following the formulation of <xref ref-type="bibr" rid="bib1.bibx18" id="text.58"/>, the problem is non-dimensionalized in space as <inline-formula><mml:math id="M39" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:mi>y</mml:mi><mml:mo>∼</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">D</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and in time <inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:mi>t</mml:mi><mml:mo>∼</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">D</mml:mi></mml:msub><mml:mo>/</mml:mo><mml:mi>U</mml:mi></mml:mrow></mml:math></inline-formula>, where <inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">D</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M43" display="inline"><mml:mi>U</mml:mi></mml:math></inline-formula> are the baroclinic deformation radius and a current magnitude scale, respectively. Also, the aspect ratio between the upper and bottom layers thicknesses, <inline-formula><mml:math id="M44" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M45" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>, is <inline-formula><mml:math id="M46" display="inline"><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>h</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. In this framework, the only parameters that vary are <inline-formula><mml:math id="M47" display="inline"><mml:mi>U</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M48" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">D</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="M49" display="inline"><mml:mi mathvariant="italic">δ</mml:mi></mml:math></inline-formula> and are chosen to be representative of the LCE described here: <inline-formula><mml:math id="M50" display="inline"><mml:mrow><mml:mi>U</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.8</mml:mn></mml:mrow></mml:math></inline-formula> m s<sup>−1</sup>, <inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="normal">D</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">50</mml:mn></mml:mrow></mml:math></inline-formula> km, and <inline-formula><mml:math id="M53" display="inline"><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">0.25</mml:mn></mml:mrow></mml:math></inline-formula>. Note that the results presented here were not sensitive to these parameters (not shown). The domain size is chosen to be a 800 km wide square, and simulations are run over a year. Simulations are integrated in either <inline-formula><mml:math id="M54" display="inline"><mml:mrow><mml:mn mathvariant="normal">128</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">128</mml:mn></mml:mrow></mml:math></inline-formula> or <inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:mn mathvariant="normal">512</mml:mn><mml:mo>×</mml:mo><mml:mn mathvariant="normal">512</mml:mn></mml:mrow></mml:math></inline-formula> point grids and are denominated as “low-resolution” or “high-resolution” runs, respectively. Time steps are adjusted to satisfy the Courant–Friedrichs–Lewy (CFL) stability criterion, which ensures numerical stability <xref ref-type="bibr" rid="bib1.bibx16" id="paren.59"><named-content content-type="pre">the propagation speed of information does not exceed the grid cell size per time step;</named-content></xref>. Small scales are damped through hyperviscosity of the order <inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> coefficient <inline-formula><mml:math id="M57" display="inline"><mml:mi mathvariant="italic">ν</mml:mi></mml:math></inline-formula> and chosen to be as small as possible <xref ref-type="bibr" rid="bib1.bibx6" id="paren.60"/>. I chose a doubly periodic domain to eliminate spurious boundary effects, as in classical numerical vortex studies <xref ref-type="bibr" rid="bib1.bibx41" id="paren.61"><named-content content-type="pre">see all the literature since</named-content></xref>.</p>
      <p id="d2e1212">In vortex stability studies, the key aspect is the initialization of the vortex. Numerous analytical models exist, with the simplest being a Gaussian. However, the choice of which quantity follows a Gaussian distribution significantly impacts the results. A Gaussian vorticity profile leads to a very stable vortex, which is not representative of realistic oceanic conditions. In contrast, a Gaussian streamfunction or velocity profile better reflects oceanic vortices, as it naturally generates a vorticity shield. This shield is crucial for the vortex's evolution and closely represents the conditions observed in our study, as seen in, e.g., Fig. <xref ref-type="fig" rid="F1"/>g. Here, I adopt this approach and initialize the upper-layer streamfunction (equivalent to the SLA) of the model as a Gaussian-like function:

          <disp-formula id="App1.Ch1.S2.E1" content-type="numbered"><label>B1</label><mml:math id="M58" display="block"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ψ</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mo>±</mml:mo><mml:mi>A</mml:mi><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:msup><mml:mfenced close=")" open="("><mml:mstyle scriptlevel="+1"><mml:mfrac><mml:mi>r</mml:mi><mml:mi>R</mml:mi></mml:mfrac></mml:mstyle></mml:mfenced><mml:mi mathvariant="italic">α</mml:mi></mml:msup></mml:mrow></mml:msup><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>

        with <inline-formula><mml:math id="M59" display="inline"><mml:mi>r</mml:mi></mml:math></inline-formula> the radial coordinate, <inline-formula><mml:math id="M60" display="inline"><mml:mi>A</mml:mi></mml:math></inline-formula> the amplitude of the eddy, <inline-formula><mml:math id="M61" display="inline"><mml:mi>R</mml:mi></mml:math></inline-formula> its radius, and <inline-formula><mml:math id="M62" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> the steepness of the eddy edges. Note that I also tested a “Mexican hat” function for <inline-formula><mml:math id="M63" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ψ</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> initialization – designed to provide both an SSH and a vorticity shield – and found similar results (not shown). I chose <inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">100</mml:mn></mml:mrow></mml:math></inline-formula> km to match the size of the LCE studied here; variations in this parameter do not affect our conclusions. Mainly, the simulations show that the presence of the shield leads to the formation of multiple satellite vortices, with their number increasing as the steepness parameter <inline-formula><mml:math id="M65" display="inline"><mml:mi mathvariant="italic">α</mml:mi></mml:math></inline-formula> increases, with no impact on the number of “coherent structures” from the resolution of the model (Fig. <xref ref-type="fig" rid="FA1"/>a–e). In particular, the case with <inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:math></inline-formula> shows that eddy can naturally become mode-4 structures, similarly as observed in SWOT data (Fig. <xref ref-type="fig" rid="F1"/>l).</p>
      <p id="d2e1328">Second, I integrate a surface quasi-geostrophic (SQG) model, part of the same code as the QG model discussed earlier, following <xref ref-type="bibr" rid="bib1.bibx6" id="text.62"/>. The SQG model is expressed in physical units, with parameters representative of typical open ocean conditions: Coriolis parameter <inline-formula><mml:math id="M67" display="inline"><mml:mrow><mml:msub><mml:mi>f</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> s<sup>−1</sup> and Brunt–Väisälä frequency <inline-formula><mml:math id="M69" display="inline"><mml:mrow><mml:msubsup><mml:mi>N</mml:mi><mml:mn mathvariant="normal">0</mml:mn><mml:mn mathvariant="normal">2</mml:mn></mml:msubsup><mml:mo>=</mml:mo><mml:mn mathvariant="normal">8</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">10</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula> s<sup>−2</sup>. I use the same numerical setup as in the QG model (resolution, viscosity, time step) and initialize it identically to Fig. <xref ref-type="fig" rid="FA1"/>d and e (<inline-formula><mml:math id="M71" display="inline"><mml:mrow><mml:mi mathvariant="italic">α</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">5</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M72" display="inline"><mml:mrow><mml:mi>R</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">100</mml:mn></mml:mrow></mml:math></inline-formula> km). In the simulation, a mode-4 structure emerges, indicating that its formation is intrinsic to the eddy's initial shape rather than the physical model. However, I also observe numerous submesoscale structures around it (Fig. <xref ref-type="fig" rid="FA1"/>f), a hallmark of SQG dynamics. This closely resembles the edges of the observed LCE, where many fronts and SCVs are detected.</p>
      <p id="d2e1436">I emphasize that the simulations presented here are intended to illustrate the dominant instability mechanism qualitatively. The subsequent evolution and timescales observed in the real ocean are highly influenced by external interactions absent from the idealized model, making direct comparisons hazardous.</p>
</app>
  </app-group><notes notes-type="codedataavailability"><title>Code and data availability</title>

      <p id="d2e1444">SWOT data can be downloaded on the AVISO website: <uri>https://www.aviso.altimetry.fr/en/my-aviso-plus.html</uri> (last accss: 2 September 2025). The numerical model is inspired by Callies et al. (2016) code available on Github: <uri>https://github.com/joernc/QGModel</uri> (last accss: 2 September 2025).</p>
  </notes><notes notes-type="competinginterests"><title>Competing interests</title>

      <p id="d2e1456">The author has declared that there are no competing interests.</p>
  </notes><notes notes-type="disclaimer"><title>Disclaimer</title>

      <p id="d2e1462">Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.</p>
  </notes><ack><title>Acknowledgements</title><p id="d2e1468">Charly de Marez was supported by a Queen Margrethe II's and Vigdís Finnbogadóttir's Interdisciplinary Research Centre on Ocean, Climate and Society (ROCS) postdoctoral fellowship. I thoroughly thank Xavier Carton, Angel Ruiz-Angulo, and Thomas Meunier for their valuable feedback and insightful comments on the manuscript. The author acknowledges the many scientists who have contributed to the long history of research in the Gulf of Mexico. Special recognition is also given to the Gulf of Mexico itself – not only for its rich and complex dynamics but also for the significance of its name, which serves as a crucial reminder of its true identity and must be protected whatever the cost.</p></ack><notes notes-type="financialsupport"><title>Financial support</title>

      <p id="d2e1473">This research was supported by a Queen Margrethe II's and Vigdís Finnbogadóttir's Interdisciplinary Research Centre on Ocean, Climate and Society (ROCS) postdoctoral fellowship.</p>
  </notes><notes notes-type="reviewstatement"><title>Review statement</title>

      <p id="d2e1479">This paper was edited by Karen J. Heywood and reviewed by two anonymous referees.</p>
  </notes><ref-list>
    <title>References</title>

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