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<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Mar. Sci.</journal-id>
<journal-title-group>
<journal-title>Frontiers in Marine Science</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Mar. Sci.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">2296-7745</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
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<article-meta>
<article-id pub-id-type="doi">10.3389/fmars.2025.1612637</article-id>
<article-version article-version-type="Version of Record" vocab="NISO-RP-8-2008"/>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Original Research</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Topographic forcing of submesoscale instability in the Antarctic Circumpolar Current</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name><surname>Ferris</surname><given-names>Laur</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="corresp" rid="c001"><sup>*</sup></xref>
<uri xlink:href="https://loop.frontiersin.org/people/3025649/overview"/>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="methodology" vocab-term-identifier="https://credit.niso.org/contributor-roles/methodology/">Methodology</role>
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<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="conceptualization" vocab-term-identifier="https://credit.niso.org/contributor-roles/conceptualization/">Conceptualization</role>
</contrib>
<contrib contrib-type="author">
<name><surname>Gong</surname><given-names>Donglai</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<uri xlink:href="https://loop.frontiersin.org/people/1746192/overview"/>
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</contrib>
<contrib contrib-type="author">
<name><surname>Klinck</surname><given-names>John</given-names></name>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<uri xlink:href="https://loop.frontiersin.org/people/1166865/overview"/>
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<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="methodology" vocab-term-identifier="https://credit.niso.org/contributor-roles/methodology/">Methodology</role>
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<aff id="aff1"><label>1</label><institution>Virginia Institute of Marine Science, William &amp; Mary</institution>, <city>Gloucester Point</city>, <state>VA</state>, <country country="us">United States</country></aff>
<aff id="aff2"><label>2</label><institution>Center for Coastal Physical Oceanography, Old Dominion University</institution>, <city>Norfolk</city>, <state>VA</state>, <country country="us">United States</country></aff>
<author-notes>
<corresp id="c001"><label>*</label>Correspondence: Laur Ferris, <email xlink:href="mailto:lnferris@vims.edu">lnferris@vims.edu</email></corresp>
</author-notes>
<pub-date publication-format="electronic" date-type="pub" iso-8601-date="2025-09-25">
<day>25</day>
<month>09</month>
<year>2025</year>
</pub-date>
<pub-date publication-format="electronic" date-type="collection">
<year>2025</year>
</pub-date>
<volume>12</volume>
<elocation-id>1612637</elocation-id>
<history>
<date date-type="received">
<day>16</day>
<month>04</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>22</day>
<month>07</month>
<year>2025</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2025 Ferris, Gong and Klinck.</copyright-statement>
<copyright-year>2025</copyright-year>
<copyright-holder>Ferris, Gong and Klinck</copyright-holder>
<license>
<ali:license_ref start_date="2025-09-25">https://creativecommons.org/licenses/by/4.0/</ali:license_ref>
<license-p>This is an open-access article distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License (CC BY)</ext-link>. The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</license-p>
</license>
</permissions>
<abstract>
<p>Subpolar frontal zones are characterized by energetic storms, intense seasonal cycles, and close connectivity with surrounding continental shelf topography. At the same time, predicting the ocean state depends on appropriate partition of resolved and parameterized dynamics, the latter of which requires understanding the dynamical processes generating diffusivity throughout the water column. While submesoscale frontal instabilities are shown to produce turbulent kinetic energy (TKE) and mixing in the surface boundary layer (SBL) of the global ocean, their development in complex dynamical regimes (e.g., elevated preexisting turbulence, large ageostrophic shear, or in proximity to topographic boundaries) is less understood. This study investigates the development of submesoscale instabilities, i.e. symmetric instability (SI) and centrifugal instability (CI), near topographic boundaries using a hindcast model of the Drake Passage and Scotia Sea region. The model suggests subsurface SI and CI are widespread along the northern continental margins of the Antarctic Circumpolar Current (ACC) due to topographic shearing of the anticyclonic side of Polar Front jets. Forced instabilities may facilitate persistent mixing along Namuncur&#xe1; - Burwood Bank, as well as in other southern (northern) hemisphere currents with low potential vorticity and a seamount or sloping topography on the left- (right-) downstream side.</p>
</abstract>
<kwd-group>
<kwd>submesoscale</kwd>
<kwd>instability</kwd>
<kwd>flow-topography interaction</kwd>
<kwd>mixing</kwd>
<kwd>Antarctic Circumpolar Current</kwd>
</kwd-group>
<funding-group>
<funding-statement>The author(s) declare financial support was received for the research and/or publication of this article. Ferris&#x2019;s effort was funded by the Virginia Institute of Marine Science (VIMS) Office of Academic Studies as well as the Applied Physics Laboratory - University of Washington Science &amp; Engineering Enrichment &amp; Development (SEED) Fellowship.</funding-statement>
</funding-group>
<counts>
<fig-count count="6"/>
<table-count count="2"/>
<equation-count count="7"/>
<ref-count count="59"/>
<page-count count="13"/>
<word-count count="5762"/>
</counts>
<custom-meta-group>
<custom-meta>
<meta-name>section-in-acceptance</meta-name>
<meta-value>Physical Oceanography</meta-value>
</custom-meta>
</custom-meta-group>
</article-meta>
</front>
<body>
<sec id="s1" sec-type="intro">
<label>1</label>
<title>Introduction</title>
<p>Mesoscale processes and turbulent mixing within the Southern Ocean play critical roles in global circulation and climate; but their exact relationship, including the relative importance of isopycnal and diapycnal processes, is still poorly understood (<xref ref-type="bibr" rid="B54">Waterhouse, 2014</xref>; <xref ref-type="bibr" rid="B47">Tamsitt et&#xa0;al., 2017</xref>). The Southern Ocean is characterized by filament-like density fronts, water mass boundaries demarcated by abrupt changes in the temperature-salinity relation which give rise to strong zonal geostrophic jets and sites of concentrated mesoscale eddying. The positions of ACC fronts and their associated geostrophic flow, eddy kinetic energy, poleward heat flux, and carbon uptake vary on seasonal to inter-annual timescales, responding to forcing changes such as the Southern Annular Mode and climatological warming (<xref ref-type="bibr" rid="B34">Meredith and Hogg, 2006</xref>; <xref ref-type="bibr" rid="B28">Lenton and Matear, 2007</xref>; <xref ref-type="bibr" rid="B29">Liau and Chao, 2017</xref>).</p>
<p>The dynamics of intense frontal regions are challenging for numerical ocean models to predict, both on operational and climatological timescales. One issue is that Reynolds Averaged Navier-Stokes (RANS)type ocean models implement mixing through diffusivity parameterizations [i.e. KPP (<xref ref-type="bibr" rid="B26">Large et&#xa0;al., 1994</xref>), <xref ref-type="bibr" rid="B33">Mellor-Yamada (1982)</xref>, Generic Length Scale (GLS)] which are generally based on vertical buoyancy and velocity gradients. Submesoscale instabilities such as SI and CI arise in part from horizontal buoyancy and velocity gradients; the unresolved mixing effects of these instabilities are not represented by traditional subgrid-scale mixing parameterizations. Additionally, some parameterizations separate physical processes into surface effects and interior effects. For example, KPP leverages boundary layer similarity scaling in the upper ocean and three interior processes (shear instability, double diffusive mixing, and internal waves). Regions where energetic currents flow through complex topography can fall outside the design conditions of these parameterizations; boundaries are known to alter stability (<xref ref-type="bibr" rid="B20">Gula et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B59">Yankovsky et&#xa0;al., 2021</xref>), allowing traditionally surface-based instabilities to occur in the ocean interior. With limited computational resources, it is advantageous to identify the processes most influential to mixing; and whether to parameterize these instabilities as SBL processes or throughout the interior in the development of next-generation climate and regional models.</p>
<p>SI has gained interest for explaining enhanced mixing at frontal jets; and arises from the same physical setup as baroclinic instability, but acts at smaller scale of 20&#x2013;500 m (<xref ref-type="bibr" rid="B8">Dong et&#xa0;al., 2021a</xref>) and in the across-front direction (<xref ref-type="bibr" rid="B40">Smyth and Carpenter, 2019</xref>). CI (<xref ref-type="bibr" rid="B24">Jiao and Dewar, 2015</xref>) occurs when absolute vorticity destabilizes the flow, independent of any destabilization by density effects. An inviscid criterion for SI in a steady geostrophic flow is <inline-formula>
<mml:math display="inline" id="im1"><mml:mrow><mml:mi>R</mml:mi><mml:mi>i</mml:mi><mml:mo>&lt;</mml:mo><mml:mo>&#xa0;</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:msub><mml:mi>&#x3b6;</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>f</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>U</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>, termed centrifugal-symmetric instability (CSI) when relative vorticity has a significant-but-insufficient role in destabilization. Notably (<xref ref-type="bibr" rid="B4">Chor et&#xa0;al., 2022</xref>) used large eddy simulations (LES) to find that CSI carries a higher mixing efficiency (the fraction of TKE that meaningfully alters the water column) than SI, indicating this less-idealized variety of submesoscale instability may play a disproportionate role in mixing some regions of the global ocean. Furthermore, external forcing can sustain SI despite its removal by shear production, buoyancy production, and dissipative processes. [Note: (<xref ref-type="bibr" rid="B58">Wienkers et&#xa0;al., 2021</xref>) examines the ratio of shear:buoyancy production as a function of front strength.] Ekman buoyancy flux (<italic>EBF</italic>), created when along-front wind stress causes an Ekman advective transport of dense water over light water, is one type forcing that can sustain baroclinic and symmetric instability. This effect can be augmented by nonlinear Ekman dynamics acting on a nonuniform vorticity field, such as a jet with an cyclonic side and an anticyclonic side (<xref ref-type="bibr" rid="B48">Thomas et&#xa0;al., 2008</xref>).</p>
<p>However, an along-front wind component is not required for SI; it is one of many agents reducing or enlarging the potential vorticity. The notable vorticity-modifying agent in our paper is topographic drag, of which several scenarios (direct and indirect) have previously been discussed in the literature. One such is <xref ref-type="bibr" rid="B59">Yankovsky et&#xa0;al. (2021)</xref>, which presented simulations of SI arising under conditions of intense vertical shear in bottom-intensified dense overflows, such that topographic drag indirectly contributes to low potential vorticity. <xref ref-type="bibr" rid="B56">Wenegrat and Thomas (2020)</xref> similarly used simulations to depict topographic drag facilitating SI via a destratifying bottom Ekman transport. <xref ref-type="bibr" rid="B20">Gula et&#xa0;al. (2016)</xref> described the direct influence of topographic drag on development of CI, where it enhances anticyclonic shear (relative vorticity) to create instability.</p>
<p>Regional models are generally too coarse to resolve growing submesoscale instabilities and are limited to showing the location of unstable structures, which can be thought of as initial conditions for a growing instability &#x2014; a turbulence-resolving model such as an LES or direct numerical simulation is required to actually quantify their impact on the water column. SI can facilitate both along-isopycnal diffusivity (as it grows) and diapycnal diffusivity (as shear or convective instability mixes away the structures produced by its growth), and is described in the literature both to destratify (<xref ref-type="bibr" rid="B19">Goldsworth et&#xa0;al., 2024</xref>) and restratify (<xref ref-type="bibr" rid="B58">Wienkers et&#xa0;al., 2021</xref>; <xref ref-type="bibr" rid="B9">Dong et&#xa0;al., 2021b</xref>) the water column. We take a moment to highlight two distinct diffusivity parameterizations for SI in the literature: (<xref ref-type="bibr" rid="B2">Bachman et&#xa0;al., 2017</xref>) which considers surfaceforced SI, and (<xref ref-type="bibr" rid="B59">Yankovsky et&#xa0;al., 2021</xref>) which considers SI throughout the water column. The Bachman parameterization, applied to the Coastal and Regional Ocean Community Model (CROCO) by (<xref ref-type="bibr" rid="B9">Dong et&#xa0;al., 2021b</xref>), treats geostrophic production by forced SI (FSI), which can occur when <italic>EBF</italic> and the surface buoyancy flux (<italic>J<sub>b</sub></italic>) sustain SI in the SBL, <inline-formula>
<mml:math display="inline" id="im2"><mml:mrow><mml:mi>E</mml:mi><mml:mi>B</mml:mi><mml:mi>F</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>J</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo>&gt;</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math></inline-formula>. Here <inline-formula>
<mml:math display="inline" id="im3"><mml:mrow><mml:mi>E</mml:mi><mml:mi>B</mml:mi><mml:mi>F</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>|</mml:mo><mml:mrow><mml:mi>&#x3c4;</mml:mi><mml:msub><mml:mi>U</mml:mi><mml:mi>z</mml:mi></mml:msub><mml:msubsup><mml:mi>&#x3c1;</mml:mi><mml:mn>0</mml:mn><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mo>|</mml:mo></mml:mrow><mml:mi>cos</mml:mi><mml:msub><mml:mi>&#x3b8;</mml:mi><mml:mi>w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, where &#x3c4; is the wind stress, and <italic>&#x3b8;</italic><sub>w</sub> is the angle of the wind relative to geostrophic shear (<italic>U<sub>z</sub></italic>). The parameterization (<xref ref-type="bibr" rid="B2">Bachman et&#xa0;al., 2017</xref>; <xref ref-type="bibr" rid="B9">Dong et&#xa0;al., 2021b</xref>) uses the bulk potential vorticity</p>
<disp-formula id="eq1"><label>(1)</label>
<mml:math display="block" id="M1"><mml:mrow><mml:mi>q</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>f</mml:mi><mml:mover accent="true"><mml:mi>k</mml:mi><mml:mo>^</mml:mo></mml:mover><mml:mo>+</mml:mo><mml:mtext>&#x2207;</mml:mtext><mml:mo>&#xd7;</mml:mo><mml:mi>u</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>&#xb7;</mml:mo><mml:mtext>&#x2207;</mml:mtext><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>z</mml:mi></mml:msub><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>f</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>U</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:msub><mml:mo>]</mml:mo><mml:mrow><mml:mi>v</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>t</mml:mi><mml:mi>i</mml:mi><mml:mi>c</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo></mml:mrow><mml:mo>[</mml:mo></mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:msub><mml:mi>U</mml:mi><mml:mi>z</mml:mi></mml:msub><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>B</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mi>V</mml:mi><mml:mi>z</mml:mi></mml:msub><mml:msub><mml:mo>]</mml:mo><mml:mrow><mml:mi>l</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>a</mml:mi><mml:mi>l</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>
</disp-formula>
<p>to identify instability (<italic>qf&lt;</italic> 0) in the SBL and estimates the associated geostrophic shear production from FSI. In contrast (<xref ref-type="bibr" rid="B59">Yankovsky et&#xa0;al., 2021</xref>), developed a parameterization for SI throughout the water column which does not rely on dimensional parameters or FSI.</p>
<p>To best parameterize submesoscale instabilities, an improved understanding of their phenomenology is needed. Several prior efforts have aimed to elucidate the role of submesoscale dynamics in complex regimes. <xref ref-type="bibr" rid="B20">Gula et&#xa0;al. (2016)</xref> used a nested Regional Ocean Modeling System (ROMS) model (&#x394;<italic>x</italic> = 200 m) to show that the anticyclonic (eastern) side of the Gulf Stream is topographically sheared by the Bahama Banks, decreasing relative vorticity (amplifying anticyclonic shear) sufficient to produce CI. <xref ref-type="bibr" rid="B7">Dewar et&#xa0;al. (2015)</xref> discussed a similar mechanism in the smaller-scale, estimating diffusivities of 10<sup>&#x2212;4</sup> m<sup>2</sup>/s due to topographically forced CI. <xref ref-type="bibr" rid="B41">St. Laurent et&#xa0;al. (2019)</xref> used a HYCOM model (&#x394;<italic>x</italic> = 1<italic>/</italic>12&#xb0;) of Palau&#x2019;s wake and a turbulence glider to show only 10% of elevated TKE is attributable to classic wind-driven shear &#x2014; the other 90% of elevated TKE likely attributable to shear or submesoscale instability associate with the relative vorticity field in Palau&#x2019;s wake. <xref ref-type="bibr" rid="B39">Simmons et&#xa0;al. (2019)</xref> discussed how vorticity structures in the wake draw energy from mean flow and feed energy to smaller scales, where instability converts this energy to TKE dissipation. <xref ref-type="bibr" rid="B36">Rosso et&#xa0;al. (2015)</xref> used a hydrostatic MITgcm model (&#x394;<italic>x</italic> = 1<italic>/</italic>80&#xb0; or 1.39 km) to study forward energy cascade in the south Indian ACC, suggesting mesoscale EKE and strain rate could be used to parameterize submesoscale vertical velocity. <xref ref-type="bibr" rid="B31">Mashayek et&#xa0;al. (2017)</xref> used nested 1/100&#xb0; model to show topographic enhancement of mixing over various hotspots in the Drake Passage and Scotia Sea, again confirming the strong role of topography in the ACC forward energy cascade. Finally, <xref ref-type="bibr" rid="B55">Wenegrat et&#xa0;al. (2018)</xref>; <xref ref-type="bibr" rid="B56">Wenegrat and Thomas (2020)</xref> discussed the importance of baroclinic instability, CI, and SI in the Ekman adjustment of bottom boundary layers over sloping topography.</p>
<p>Observations of the Kuroshio (<xref ref-type="bibr" rid="B6">D&#x2019;Asaro et&#xa0;al., 2011</xref>) and Gulf Stream (<xref ref-type="bibr" rid="B50">Thomas et&#xa0;al., 2013</xref>, <xref ref-type="bibr" rid="B49">Thomas et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B51">Todd et&#xa0;al., 2016</xref>) have suggested SI might be ubiquitous to the ACC. There are limited observations of symmetric instability in the ACC, but one instance is <xref ref-type="bibr" rid="B1">Adams et&#xa0;al. (2017)</xref>, who observed a variety of submesoscale instabilities in the upper 200 m of a mesoscale cyclonic eddy in the Scotia Sea during the SMILES (Surface Mixed Layer Evolution at Submesoscales) project. Submesoscale instabilities resulting from the interaction of mesoscale eddies with the Polar Front (PF) were shown to generate large vertical velocities (&#x223c;100 m/day) and water mass modification associated with the Sub Antarctic Mode Water (SAMW). The largest patch of CI was on the edge of a warm core ring closest to sloping bathymetry at 100&#x2013;150 m depth, with other areas dominated by gravitational, symmetric, and mixed instabilities. The northern edge of the eddy was within 1/2&#xb0; of the North Scotia Ridge, such that it is compelling to consider whether topography influenced these instabilities. <xref ref-type="bibr" rid="B35">Naveira Garabato et&#xa0;al. (2019)</xref> used a microstructure-equipped AUV in an along-slope current of South Orkney Plateau, Antarctica, to observe that submesoscale instabilities (including SI) drive a cross-current secondary circulation and expedite the transformation of water through enhanced boundary layer-interior exchange. It seems the flanks of geostrophic currents, where horizontal shears are greatest, may be more active sources of submesoscale instability than the geostrophic fronts themselves.</p>
<p>A November 2017 - February 2018 glider program, Autonomous Sampling of Southern Ocean Mixing (AUSSOM), also measured moderately elevated TKE dissipation rates where the ACC flows past Namuncur&#xe1; - Burwood Bank (<xref ref-type="fig" rid="f1"><bold>Figure&#xa0;1</bold></xref>). This turbulence record shows elevated turbulence in three distinct regimes: the SBL, the subsurface ocean near the Bank (along both the continental rise and over the shelf), and subsurface open ocean (1&#x2013;12 December). For further details about AUSSOM the reader is referred to <xref ref-type="bibr" rid="B12">Ferris (2022)</xref> and <xref ref-type="bibr" rid="B14">Ferris et&#xa0;al (2022a)</xref>, <xref ref-type="bibr" rid="B15">Ferris et&#xa0;al (2022b)</xref>), and for further details about glider-based turbulence measurement, the reader is referred to <xref ref-type="bibr" rid="B11">Fer et&#xa0;al. (2014)</xref> and <xref ref-type="bibr" rid="B42">St. Laurent and Merrifield (2017)</xref>. In this study, we use vorticity and buoyancy flux fields from a 1-km ROMS hindcast (developed in support of AUSSOM) to show that topographic shearing drives CI and CSI when the PF veers close to the northern boundary of the ACC in the Drake Passage and Scotia Sea, providing one mechanism for elevated turbulence along Namuncur&#xe1; - Burwood Bank; a mechanism similar to that of <xref ref-type="bibr" rid="B20">Gula et&#xa0;al. (2016)</xref> for CI in the Gulf Stream. More generally, this represents a pathway for submesoscale frontal instabilities to supply energy to the ACC microscale.</p>
<fig id="f1" position="float">
<label>Figure&#xa0;1</label>
<caption>
<p><bold>(a)</bold> Track of Slocum glider Starbuck along the Polar Front (PF) in Drake Passage and Scotia Sea during the AUSSOM project in late 2017 and early 2018. Temperature from ROMS is nested in temperature from 1/12&#xb0; Operational Mercator. Note that the PF can merge with the Subantarctic Front in this region. <bold>(b)</bold> Showing observations of TKE dissipation rate collected by the glider. Elevated mixing is observed in the SBL, the subsurface core of the PF, and in proximity to sloping bathymetry (24-November onward). <bold>(c)</bold> A zoomed-in subset of <bold>(b)</bold> highlighting TKE dissipation near the bank.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-12-1612637-g001.tif">
<alt-text content-type="machine-generated">Map showing AUSOM Glider track and ROMS temperature data on December 1, 2017. The map spans 65&#xba;S to 50&#xba;S and 75&#xba;W to 50&#xba;W, showing green glider paths over a color gradient from 0 to 9 degrees Celsius. Key indicates ROMS domain, instantaneous glider position, and whether microstructure was sampled. Below, graph displays turbulent kinetic energy dissipation rate over time and depth, with a color bar indicating dissipation values.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s2">
<label>2</label>
<title>Methods</title>
<p>For this basin-scale analysis, we use a criterion <xref ref-type="disp-formula" rid="eq2">Equation 2</xref> for overturning instability (<xref ref-type="bibr" rid="B21">Hoskins, 1974</xref>; <xref ref-type="bibr" rid="B50">Thomas et&#xa0;al., 2013</xref>) based on a balanced form of the Richardson number <inline-formula>
<mml:math display="inline" id="im4"><mml:mrow><mml:mi>R</mml:mi><mml:mi>i</mml:mi><mml:mo>&#xa0;</mml:mo><mml:mo>=</mml:mo><mml:mo>&#xa0;</mml:mo><mml:msub><mml:mi>B</mml:mi><mml:mi>z</mml:mi></mml:msub><mml:mo stretchy="false">/</mml:mo><mml:mo>&#xa0;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mi>U</mml:mi><mml:mi>z</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo>&#xa0;</mml:mo><mml:mo>+</mml:mo><mml:mo>&#xa0;</mml:mo><mml:msubsup><mml:mi>V</mml:mi><mml:mi>z</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></inline-formula> which assumes the dominance of geostrophic dynamics, <inline-formula>
<mml:math display="inline" id="im5"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>f</mml:mi><mml:msub><mml:mi>U</mml:mi><mml:mi>z</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>:</p>
<disp-formula id="eq2"><label>(2)</label>
<mml:math display="block" id="M2"><mml:mrow><mml:mi>R</mml:mi><mml:msub><mml:mi>i</mml:mi><mml:mi>B</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:msubsup><mml:mi>U</mml:mi><mml:mi>z</mml:mi><mml:mrow><mml:mi>G</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msubsup><mml:mo>+</mml:mo><mml:msubsup><mml:mi>V</mml:mi><mml:mi>z</mml:mi><mml:mrow><mml:mi>G</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:mfrac><mml:mo>&#x2261;</mml:mo><mml:mfrac><mml:mrow><mml:msup><mml:mi>f</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:msup><mml:mi>N</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:msub><mml:mtext>&#x2207;</mml:mtext><mml:mi>h</mml:mi></mml:msub><mml:mi>b</mml:mi><mml:msup><mml:mo>|</mml:mo><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mfrac><mml:mo>&lt;</mml:mo><mml:mfrac><mml:mi>f</mml:mi><mml:mrow><mml:msub><mml:mi>&#x3b6;</mml:mi><mml:mi>a</mml:mi></mml:msub></mml:mrow></mml:mfrac><mml:mo>.</mml:mo></mml:mrow></mml:math>
</disp-formula>
<p>Excluding barotropic inertial/centrifugal instabilities <inline-formula>
<mml:math display="inline" id="im6"><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>f</mml:mi><mml:msub><mml:mi>&#x3b6;</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:mo>&lt;</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></inline-formula> ,overturning instabilities arise when <inline-formula>
<mml:math display="inline" id="im7"><mml:mrow><mml:msub><mml:mtext>&#x3a6;</mml:mtext><mml:mrow><mml:mi>R</mml:mi><mml:msub><mml:mi>i</mml:mi><mml:mi>B</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>&lt;</mml:mo><mml:msub><mml:mtext>&#x3a6;</mml:mtext><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, where <inline-formula>
<mml:math display="inline" id="im8"><mml:mrow><mml:msub><mml:mtext>&#x3a6;</mml:mtext><mml:mrow><mml:mi>R</mml:mi><mml:msub><mml:mi>i</mml:mi><mml:mi>B</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mtext>tan</mml:mtext></mml:mrow><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">/</mml:mo><mml:mi>R</mml:mi><mml:msub><mml:mi>i</mml:mi><mml:mi>B</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> is the balanced Richardson number angle and <inline-formula>
<mml:math display="inline" id="im9"><mml:mrow><mml:msub><mml:mtext>&#x3a6;</mml:mtext><mml:mi>c</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mtext>tan</mml:mtext></mml:mrow><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>&#x3b6;</mml:mi><mml:mi>a</mml:mi></mml:msub><mml:mo stretchy="false">/</mml:mo><mml:mi>f</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> is a critical angle (<xref ref-type="bibr" rid="B50">Thomas et&#xa0;al., 2013</xref>). Here &#x3b6;<sub>a</sub> is the absolute vorticity and <inline-formula>
<mml:math display="inline" id="im10"><mml:mrow><mml:mi>b</mml:mi><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>g</mml:mi><mml:msub><mml:mi>&#x3c1;</mml:mi><mml:mi>&#x3b8;</mml:mi></mml:msub><mml:mo stretchy="false">/</mml:mo><mml:msub><mml:mi>&#x3c1;</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula>. The inverse tangent function can be approximated as a piecewise function such that discrete instability types are identified by the relative dominance of destabilizing characteristics, useful for the efficient identification of instability types (<xref ref-type="table" rid="T1"><bold>Table&#xa0;1</bold></xref> reproduced from <xref ref-type="bibr" rid="B50">Thomas et&#xa0;al., 2013</xref>).</p>
<table-wrap id="T1" position="float">
<label>Table&#xa0;1</label>
<caption>
<p>Instability criteria.</p>
</caption>
<table frame="hsides">
<thead>
<tr>
<th valign="top" align="left">Type</th>
<th valign="top" align="left">Criteria</th>
</tr>
</thead>
<tbody>
<tr>
<td valign="top" align="left">Centrifugal Instability (CI)</td>
<td valign="top" align="left"><italic>f&#x3b6;<sub>a</sub></italic> &lt; 0 and <italic>B<sub>z</sub></italic> &gt; 0</td>
</tr>
<tr>
<td valign="top" align="left">Gravitational Instability (GI)</td>
<td valign="top" align="left">&#x2212;180 &lt; &#x3a6;<italic>Ri<sub>B</sub></italic> &lt; &#x2212;135</td>
</tr>
<tr>
<td valign="top" align="left">Gravitational-Symmetric Instability (GSI)</td>
<td valign="top" align="left">&#x2212;135 &lt; &#x3a6;<italic>Ri<sub>B</sub></italic> &lt; &#x2212;90</td>
</tr>
<tr>
<td valign="top" align="left">Symmetric Instability (SI)</td>
<td valign="top" align="left">&#x2212;90 &lt; &#x3a6;<italic>Ri<sub>B</sub></italic> &lt; &#x3a6;<italic><sub>c</sub></italic> and &#x3a6;<italic><sub>c</sub></italic> &lt; &#x2212;45 <bold>or</bold><break/>&#x2212;90 &lt; &#x3a6;<italic>Ri<sub>B</sub></italic> &lt; &#x2212;45 and &#x2212; 45 &lt; &#x3a6;<italic><sub>c</sub></italic></td>
</tr>
<tr>
<td valign="top" align="left">Centrifugal-Symmetric Instability (CSI)</td>
<td valign="top" align="left">&#x2212;45 &lt; &#x3a6;<italic>Ri<sub>B</sub></italic> &lt; &#x3a6;<italic><sub>c</sub></italic> and &#x2212; 45 &lt; &#x3a6;<italic><sub>c</sub></italic></td>
</tr>
</tbody>
</table>
</table-wrap>
<p>Model output with 1-km, 3-hr resolution, and 50 sigma (<italic>&#x3c3;</italic>) layers was produced using the Regional Ocean Modeling System (ROMS), a free-surface, hydrostatic, primitive equation model discretized with a terrain following vertical coordinate system (<xref ref-type="bibr" rid="B38">Shchepetkin and McWilliams, 2005</xref>). Runs were initialized every 7 days and run for 10 days, covering a period from 12-November-2017 through 29-December-2017. The model was initialized using 1/12&#xb0; resolution Operational Mercator (GLOBAL_ANALYSIS_FORECAST_PHY_001_024) and radiation/nudging lateral boundary conditions and a 3-day relaxation timescale (<xref ref-type="bibr" rid="B30">Marchesiello et&#xa0;al., 2001</xref>). Flux forcing was computed every 3 hours with turbulent fluxes calculated from bulk formulae (<xref ref-type="bibr" rid="B10">Fairall et&#xa0;al., 1996</xref>; <xref ref-type="bibr" rid="B27">Large and Pond, 1981</xref>) using the atmospheric state obtained from JRA-55 (<xref ref-type="bibr" rid="B52">Tsujino et&#xa0;al., 2018</xref>), and no tidal forcing was imposed. The model utilized an orthogonal curvilinear grid that tracks latitude/longitude lines. Tracers and momentum use 3rd-order upstream-biased advection in the horizontal, and 4th-order centered differences advection in_the vertical. The model used GLS vertical mixing parameterization for turbulent mixing of momentum and tracers (<xref ref-type="bibr" rid="B53">Warner et&#xa0;al., 2005</xref>); with the <xref ref-type="bibr" rid="B25">Kantha and Clayson (1994)</xref> stability function, <xref ref-type="bibr" rid="B5">Craig and Banner (1994)</xref> wave breaking surface flux, and Charnok surface roughness from wind stress (<xref ref-type="bibr" rid="B3">Carniel et&#xa0;al., 2009</xref>). Horizontal diffusion of tracers and momentum were 2 m<sup>2</sup>/s and 3 m<sup>2</sup>/s respectively, with quadratic bottom friction coefficient of 0.003.</p>
<p>Upwind advection schemes contain implicit smoothing; dynamical processes below 5-km (rather than 2-km) are not well represented due to smoothing over the stencil, staggered grids, and time stepping. A limitation of using the 1-km ROMS model to study instability is its resolution constraints; submesoscale instabilities undoubtedly exist below the scales represented in the model. While symmetrically unstable flows may persist in the ocean due to forcing (e.g., FSI), another limitation of the model is that instabilities can persist longer in the model than the ocean due to lack of removal mechanisms (either a resolved forward energy cascade, or a parameterization for the unresolved forward energy cascade). We are confident that the westward velocity anomalies (relative to geostrophic flow) along the Bank which decrease stability are not simply pressure gradient errors (<xref ref-type="bibr" rid="B32">Mellor et&#xa0;al., 1998</xref>); which would manifest as a spurious addition of &#x223c;0.01-0.1 m/s in the same direction as the geostrophic current (eastward, with the coast to the left). We also validate the results using a feature model to demonstrate the physical conditions leading to submesoscale instability (<xref ref-type="app" rid="app1"><bold>Appendix</bold></xref>).</p>
<p>Vertical buoyancy (<italic>B</italic>) and velocity (<italic>U,V)</italic> profiles are linearly interpolated from <italic>&#x3c3;</italic>-coordinates to a uniform vertical grid (&#x394;<italic>z</italic> = 5 m) before calculation of spatial derivatives and the subsequent application of instability criteria (<xref ref-type="table" rid="T1"><bold>Table&#xa0;1</bold></xref>). The distribution of instability is examined from the perspective of meridional sections (conducive to study of the mainly-zonal PF jet), as well as the full 3-D domain. The latitude (<italic>&#x3d5;</italic>) and velocity of the PF jet were obtained at the location of the maximum eastward component of velocity <italic>U</italic>(<italic>&#x3b8;,&#x3d5;,z</italic>) north of 56.5&#xb0;S and within the longitudinal range for which the front and associated jet are dominantly zonal, 63.0<sup>&#xb0;</sup>W<italic>&lt; &#x3b8; &lt;</italic> 60.0&#xb0;W. This region is selected for two reasons: The first is for ease of calculation on the model&#x2019;s original grid, thus eliminating the step of projecting the jet velocity in the direction parallel to the coast while seeking the point of maximum along-coast velocity on a rotated grid. The second is to avoid obscuring signals in a basin-scale average. The jet can be different distances from the bank along different parts of the Drake Passage and Scotia Sea, which could blur regional trends in instability if examined in a basin-averaged sense. The purpose of the latitudinal constraint is to avoid misidentifying the SACCF jet core or (secondary filaments associated with the PF) as the PF jet core. A possible limitation of this method is that it neglects slight curvatures (relative angle) of Namuncur&#xe1; - Burwood Bank and the PF jet, reducing the precision with which the reported latitude in 5c describes the jet&#x2019;s proximity to the bank throughout the entire white box. We use longitude 60.5<sup>&#xb0;</sup>W to illustrate meridional sections, but its features are common to meridional slices where the PF jet is principally zonal.</p>
</sec>
<sec id="s3" sec-type="results">
<label>3</label>
<title>Results</title>
<p>As <xref ref-type="bibr" rid="B6">D&#x2019;Asaro et&#xa0;al. (2011)</xref> and <xref ref-type="bibr" rid="B50">Thomas et&#xa0;al. (2013)</xref> hypothesized, submesoscale instabilities including CI, CSI, and SI are present in the upper ocean of the ACC (<xref ref-type="fig" rid="f2"><bold>Figure&#xa0;2a</bold></xref>), both at the abrupt lateral buoyancy gradients of PF filaments and where submesoscale vortices are generated by interaction between the ACC and Tierra del Fuego and advected eastward. In the subsurface (<xref ref-type="fig" rid="f2"><bold>Figure&#xa0;2b</bold></xref>), instabilities concentrate on the north side of the zonal jet (as predicted by geostrophic instability theory), but are tied to topography; these instabilities are found where the PF jet experiences topographic drag along Namuncur&#xe1; - Burwood Bank. The position of the PF jet (<xref ref-type="fig" rid="f3"><bold>Figure&#xa0;3</bold></xref>), namely, its proximity to the continental rise, controls the amount of subsurface CI, CSI, and SI. In general, a southern (northern) hemisphere process causing an increase (decrease) in relative vorticity increases (decreases) the potential vorticity toward symmetrically instability. Here, topographic drag on the north edge of the ACC (or alternatively, the southern flank of an abyssal feature) increases horizontal shear to create instability.</p>
<fig id="f2" position="float">
<label>Figure&#xa0;2</label>
<caption>
<p>Showing unstable nodes in the <bold>(a)</bold> upper 100 m and <bold>(b)</bold> lower 100&#x2013;4500 m for a timestep (01-Dec-2017) of the 3-D model domain; including gravitational (GI, blue), gravitational-symmetric (GSI, gray), centrifugal (CI, green), centrifugal-symmetric CSI, (red), and symmetric (SI, yellow) instability.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-12-1612637-g002.tif">
<alt-text content-type="machine-generated">3D diagrams depicting topographic data overlaid with the location of instabilities above 100 m depth. Panel (a) shows swirling currents colored by instability type near Tierra del Fuego and the Western Antarctic Peninsula, with meridional slice locations and depth notes. Panel (b) displays subsurface instabilities.</alt-text>
</graphic>
</fig>
<fig id="f3" position="float">
<label>Figure&#xa0;3</label>
<caption>
<p>Phenomenology of centrifugal (CI, green), centrifugal-symmetric (CSI, red), symmetric (SI, yellow), gravitational-symmetric (GSI, gray), and gravitational (GI, blue) instabilities at 60.5&#xb0;W (dotted line in <xref ref-type="fig" rid="f2"><bold>Figure&#xa0;2</bold></xref>) for states of the PF jet with contours of eastward velocity (<italic>U</italic>). <bold>(a)</bold> Showing SI and CSI in the SBL, associated with Polar Front filaments. <bold>(b, c)</bold> Showing CSI, CI, and the added third characteristic in the subsurface, associated with flow-topography interaction along Tierra del Fuego and Namuncur&#xe1; Burwood Bank.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-12-1612637-g003.tif">
<alt-text content-type="machine-generated">Color-contoured plots illustrating water velocity at a latitude section of 60.5&#xb0;W over time along the bank. Each panel represents a different date: (a) November 30, 2017, (b) December 4, 2017, and (c) December 15, 2017. Depth in meters is on the vertical axis and latitude on the horizontal. Velocity is measured in meters per second with color shading: red indicates positive, blue negative, with contour lines marking variations. Instabilities are overlaid as colored dots.</alt-text>
</graphic>
</fig>
<p>The potential vorticity <italic>q</italic><xref ref-type="disp-formula" rid="eq1">Equation 1</xref> in <xref ref-type="fig" rid="f3"><bold>Figure&#xa0;3</bold></xref> is decomposed into individual terms (<xref ref-type="fig" rid="f4"><bold>Figure&#xa0;4</bold></xref>). We offer general context for these terms. <italic>q</italic> is the component of the absolute vorticity vector oriented with the buoyancy gradient (usually near-vertical in stably stratified fluids). Strong stratification <italic>B<sub>z</sub></italic>, large-magnitude planetary vorticity <italic>f</italic>, and relative vorticity in the same direction as <italic>f</italic> all reinforce the stability of the spinning column of fluid. In an adiabatic, frictionless flow <italic>q</italic> is materially conserved such that a fluid column moving toward weaker stratification or lower latitude must spin faster (<xref ref-type="bibr" rid="B22">Hoskins, 1997</xref>), which is accomplished by <italic>stretching</italic> of the column in the absence of viscosity. The spin can also be influenced directly by mechanical forcing. <italic>Tilting</italic> describes the action of vertical shear <italic>U<sub>z</sub>,V<sub>z</sub></italic> to tip the horizontal vorticity. The decomposition in <xref ref-type="fig" rid="f4"><bold>Figure&#xa0;4</bold></xref> illustrates that the positive potential vorticity required for instability in the southern hemisphere is produced when vorticity of the fluid is spun in the anticyclonic direction (<xref ref-type="fig" rid="f4"><bold>Figure&#xa0;4b</bold></xref>). Conversely, SI at open-ocean fronts is dependent on weak stratification (see pale layer in <xref ref-type="fig" rid="f4"><bold>Figure&#xa0;4a</bold></xref>) for the production of net-positive potential vorticity and is thus confined to the weakly stratified SBL (&#x223c;0&#x2013;100 m).</p>
<fig id="f4" position="float">
<label>Figure&#xa0;4</label>
<caption>
<p><bold>(a)</bold> Stretching related to planetary vorticity, <bold>(b)</bold> stretching related to relative vorticity, and <bold>(c)</bold> tilting terms [s<sup>&#x2212;3</sup>] of Ertel potential vorticity (<italic>q</italic>, <xref ref-type="disp-formula" rid="eq1">Equation 1</xref>) for the boundary region in 3c, where <italic>qf&lt;</italic> 0 is unstable. Note axes have changed to zoom in on the depth and latitudinal range of interest. Positive values (red tones) are destabilizing, and negative values (blue tones) are stabilizing. The term illustrated in <bold>(b, a)</bold> is the primary driver of CSI (GSI). SI arises from combined effects of stretching <bold>(a, b)</bold> and tilting <bold>(c)</bold>. Ribbon-like features are numerical artifacts typical of <italic>&#x3c3;</italic>-coordinate models.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-12-1612637-g004.tif">
<alt-text content-type="machine-generated">Three-panel contour plot showing a partitioning of ertel potential vorticity terms on December 15, 2017, at 12:00. Each panel illustrates depth against latitude from -55.1 to -54.7 degrees South. Panel (a) shows stretching with B_zf, featuring blue gradients. Panel (b) shows stretching with B_z(V_x - U_y) in red and blue gradients. Panel (c) depicts tilting with B_z(U_y^G - V_x^G) in red gradients. Each panel includes various colored markers at different depths indicating the location of instabilities. A color bar on the right indicates values from -1 to 1 times 10^{-9} in s^-3. Black areas depict the ocean floor.</alt-text>
</graphic>
</fig>
<p>For the subset of the domain where the PF jet is principally zonal (see (Methods) and box in <xref ref-type="fig" rid="f5"><bold>Figure&#xa0;5a</bold></xref>) we identify submesoscale instabilities (<xref ref-type="fig" rid="f5"><bold>Figure&#xa0;5b</bold></xref>) in relation to latitude and speed of the PF (<xref ref-type="fig" rid="f5"><bold>Figure&#xa0;5c</bold></xref>). Separating the domain into the shallow and subsurface ocean (<xref ref-type="fig" rid="f5"><bold>Figures&#xa0;5d, e</bold></xref>) demonstrates two distinct instability regimes: an SBL dominated by classic shear-convective instability, and a subsurface ocean where CI and CSI contribute more greatly to the instability budget.</p>
<fig id="f5" position="float">
<label>Figure&#xa0;5</label>
<caption>
<p>Instability compared to frontal jet variability. Showing <bold>(a)</bold> the region of instability identification (white box) superimposed over a top-down snapshot of the model (specifically the timestep in <xref ref-type="fig" rid="f2"><bold>Figure&#xa0;2b</bold></xref>); <bold>(b)</bold> the number of uniformly interpolated grid nodes which are unstable to stratified shear instability (SSI), GI, GSI, SI, CSI, and CI; and <bold>(c)</bold> latitude and speed of the jet core. Namuncur&#xe1; - Burwood Bank is located at &#x223c;55&#xb0;S. Additionally showing the relative prevalence of each instability type identified in both <bold>(d)</bold> the subsurface ocean and <bold>(e)</bold> the upper 100 m of the region. Note vertical discontinuities in <bold>(d)</bold> reflect the use of multiple model runs to cover the study period.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-12-1612637-g005.tif">
<alt-text content-type="machine-generated">Map and graphs analyzing frontal jet dynamics. Panel (a) shows a map with zones of frontal jet identification. Panel (b) displays a line graph of unstable nodes over time. Panel (c) illustrates latitude and speed of the frontal jet. Panels (d) and (e) show instability percentages below and above 100 meters, respectively, with varied lines indicating the prevalence of instability types.</alt-text>
</graphic>
</fig>
<p>In the subsurface ocean (<xref ref-type="fig" rid="f5"><bold>Figure&#xa0;5d</bold></xref>), the location of the PF jet and the associated mesoscale eddy present in the model (<xref ref-type="fig" rid="f1"><bold>Figures&#xa0;1a</bold></xref>, <xref ref-type="fig" rid="f5"><bold>5a</bold></xref> - box) control the relative role of each instability type to which the flow is predisposed. While the PF jet is shifted southward in late November, CI and CSI comprise about 10% of all overturning instabilities (as defined in the <xref ref-type="fig" rid="f5"><bold>Figure&#xa0;5</bold></xref> caption). While the PF shifts northward toward Namuncura&#xb4; - Burwood Bank (&#x223c;55&#xb0;S) in the beginning of December, their relative role increases to about 30% and dominates the subsurface instability budget. Conversely, GI decreases as the front and mesoscale eddy shift northward. The GI arises in the modeled abyss (<xref ref-type="fig" rid="f2"><bold>Figure&#xa0;2b</bold></xref>) when deep-reaching flow of the mesoscale eddy stirs dense bottom water equatorward to overlie lighter water; its setup depends on the proximity of the eddy to the bottom water at its poleward source. Its possible importance to abyssal mixing is beyond the scope of this paper but is worthy of future inquiry.</p>
<p>In the SBL (<xref ref-type="fig" rid="f5"><bold>Figure&#xa0;5e</bold></xref>), the relative prevalence of each instability type is characterized by episodic surface evolution (<xref ref-type="bibr" rid="B14">Ferris et&#xa0;al., 2022a</xref>) as well as a diurnal oscillation produced by convective forcing in localized regions of the domain. The diurnal oscillation augments the total amount of both GI and GSI in the SBL and juxtaposes the steady nature of instability in the subsurface ocean (<xref ref-type="fig" rid="f5"><bold>Figure&#xa0;5d</bold></xref>) &#x2014; as with FSI due to winds (<xref ref-type="bibr" rid="B9">Dong et&#xa0;al., 2021b</xref>), topographic drag provides a mechanism for sustained overturning instability in the subsurface ocean. It is worth underscoring that analytical criteria in <xref ref-type="table" rid="T1"><bold>Table&#xa0;1</bold></xref> are derived for a steady flow, such that they are meaningful only if instabilities grow on a timescale faster than the timescale at which the flow evolves. Diurnal variation of SI, GI, and GSI (<xref ref-type="fig" rid="f5"><bold>Figure&#xa0;5e</bold></xref>) implies that some perceived instability in the SBL is transient and vanishes (by cessation of convective forcing and restratification) before undergoing forward energy cascade, such that some of the instability in <xref ref-type="fig" rid="f5"><bold>Figure&#xa0;5e</bold></xref> is not physically meaningful. In other words, a convective instability arising in the final hours of night may not have time to grow before the SBL is stabilized by the arrival of day.</p>
</sec>
<sec id="s4" sec-type="discussion">
<label>4</label>
<title>Discussion</title>
<p>Submesoscale instability is found at two major sites in the ACC: in the weakly stratified SBL, and in the subsurface ocean near lateral boundaries (or equivalently, sloping topography). The amount of subsurface submesoscale instability arising in ACC jets depends on their location with respect to topography, indicating that the importance of submesoscale instability to forward energy cascade in the ACC depends on temporal variation of the PF (unlike SBL instabilities which are not tied to geography of the PF). Furthermore, topographic shearing of the PF jet presents a mechanism for sustained CI, CSI, and SI (analogous to FSI in the upper ocean). Both atmospheric changes, such as the Southern Annular Mode and the El Nino&#x2dc; Southern Oscillation (ENSO), and internal dynamical variabilities alter the position of the ACC&#x2019;s frontal jets on an intra-annual to inter-annual timescale (<xref ref-type="bibr" rid="B18">Gille et&#xa0;al., 2016</xref>). Altering the latitude of the ACC fronts with respect to Southern Ocean topography likely impacts the role of CI, CSI, and SI in mixing near surface and topographic boundaries (this study); as well as that of more ubiquitous internal wave processes [see Figures&#xa0;4, 5 of <xref ref-type="bibr" rid="B43">St. Laurent et&#xa0;al. (2012)</xref>; <xref ref-type="bibr" rid="B54">Waterhouse (2014)</xref>] which impact vertical heat, carbon, and nutrient flux throughout the Southern Ocean.</p>
<p>Our results inspire us to take an intellectual leap and speculate that submesoscale instabilities may play a role in the formation of Antarctic Intermediate Water (AAIW), a process that is not well understood. As part of the upper return cell of the Atlantic Meridional Overturning Circulation (<xref ref-type="bibr" rid="B46">Talley, 2013</xref>), air-sea exchange and interior mixing transform North Atlantic Deep Water (NADW) first into Subantarctic Mode Water (SAMW) and then into Antarctic Intermediate Water (AAIW). At the northern edge of the ACC in the vicinity of Namuncur&#xe1; - Burwood Bank, a thick layer of SAWM overlies low-salinity AAIW, which overlies Upper Circumpolar Deep Water (UCDW). The Scotia Sea east of the Drake Passage is believed to be a critical site of SAMW and AAIW modification and subduction (<xref ref-type="bibr" rid="B45">Talley, 1996</xref>; <xref ref-type="bibr" rid="B37">Sall&#xe9;e et&#xa0;al., 2010</xref>), but little is known about their exact formation mechanisms. The CI, CSI, and SI discussed in this paper arise in the depth range appropriate for mixing AAIW with UCDW and SAMW (see Figure&#xa0;1 of <xref ref-type="bibr" rid="B44">Struve et&#xa0;al., 2020</xref>). After observing a rich submesoscale frontal structure and upwelling/downwelling rates of O(100) m/day east of the Drake Passage, <xref ref-type="bibr" rid="B1">Adams et&#xa0;al. (2017)</xref> remarked that submesoscale processes might be critical for the transformation and subduction of mode and intermediate waters. We agree that further observations or turbulence-resolving models are needed to understand the significance of these instabilities at the northern continental margins of the ACC.</p>
<p>We ask whether some of the near-boundary elevated TKE (over rough topography and along continental margins) which was historically attributed to internal waves could be, in part, from submesoscale instabilities undergoing forward energy cascade. However, this is not the first finding of topographic shearing facilitating the forward energy cascade by producing submesoscale instabilities in a major current; (<xref ref-type="bibr" rid="B20">Gula et&#xa0;al., 2016</xref>) observed a similar mechanism. CI, CSI, and SI are created on the anticyclonic side of the ACC when topographic drag increases relative vorticity enough to destabilize the flow. If presence of northern boundary controls the development of instability, a natural conclusion is that the Drake Passage and Scotia Sea region are unique to the rest of the ACC (perhaps with the exceptions of the Agulhas Bank and Campbell Plateau); however, other features such as the Antarctic Slope Current and Kerguelen Plateau (as well as submerged seamounts in currents across the global ocean, such as the New England Seamount Chain in the Gulf Stream) provide topographic drag and are thus candidates for topographic forcing of submesoscale instability. Despite being tied to specific topographic features, evidence for the spatial inhomogeneity of Southern Ocean mixing (<xref ref-type="bibr" rid="B57">Whalen et&#xa0;al., 2015</xref>; <xref ref-type="bibr" rid="B47">Tamsitt et&#xa0;al., 2017</xref>) shows that the spatial extent of a particular mixing mechanism does not equate to its overall impact. Topographically-sheared instabilities in the ACC may disproportionately affect mixing.</p>
<p>It is worth noting, however, that a significant amount of mixing in the Southern Ocean, especially in the subsurface open ocean, is <italic>not</italic> due to topographically forced CI, CSI, and SI &#x2014; or any kind of submesoscale instability (<xref ref-type="bibr" rid="B14">Ferris et&#xa0;al., 2022a</xref>). We briefly revisit the glider data (<xref ref-type="fig" rid="f1"><bold>Figure&#xa0;1b</bold></xref>), which shows turbulence in the SBL and subsurface ocean near the Bank (regimes where submesoscale instability occurs); as well as an unidentified patch of turbulence in the subsurface open ocean. The latter is likely not from submesoscale instability based on our analysis. While the amount of TKE produced by SI in the SBL is indeed consistent with the levels of turbulence observed by the glider (<xref ref-type="fig" rid="f6"><bold>Figure&#xa0;6</bold></xref>), this subsurface feature cannot be attributable to CI, CSI, or SI due to the limited vertical influence (depth range 0&lt; <italic>z&lt;</italic> 100 m) of these instabilities away from topographic boundaries. We speculate it is related to internal wave interactions at the margins of Polar Front jets.</p>
<fig id="f6" position="float">
<label>Figure&#xa0;6</label>
<caption>
<p>Estimated geostrophic shear production for the timestep in <xref ref-type="fig" rid="f2"><bold>Figure&#xa0;2</bold></xref> (01-Dec-2017), estimated after (<xref ref-type="bibr" rid="B50">Thomas et&#xa0;al., 2013</xref>; <xref ref-type="bibr" rid="B2">Bachman et&#xa0;al., 2017</xref>; <xref ref-type="bibr" rid="B9">Dong et&#xa0;al., 2021b</xref>). Bathymetric contours are underlaid at 300-m intervals and the instantaneous location of the glider (<xref ref-type="fig" rid="f1"><bold>Figure&#xa0;1b</bold></xref> is marked with a cross.</p>
</caption>
<graphic mimetype="image" mime-subtype="tiff" xlink:href="fmars-12-1612637-g006.tif">
<alt-text content-type="machine-generated">Map showing estimated surface geostrophic shear production in watts per kilogram across specific latitudes and longitudes. A rainbow color gradient from blue to red represents the intensity of shear production, with blue indicating lower values and red higher ones. Contour lines illustrate underlying topography, and an 'X' marks the location of the glider during the modeled timestep.</alt-text>
</graphic>
</fig>
<p>We have provided insight into the relative role and spatial arrangement of symmetric instabilities in the Southern Ocean, finding that submesoscale overturning instabilities may be as important along the topographic boundaries of the ACC as they are at fronts in the SBL of the open ocean. This finding is relevant to other energetic currents rich in frontal structure; instability analysis of the Kuroshio and Gulf Stream are relatively uncommon similar to the ACC, and there has been little submesoscale instability work in the subarctic (which is similarly rich in energetic filaments, complex topography, and sharp density fronts). The inclusion of topographically sheared submesoscale instabilities may be important for modeling ocean structure in several coastal and littoral regions of the world. Meanwhile, the overall velocity structure in many of these regions is altered by tides with short periods or diurnal convection, complicating the applicability of existing balanced frameworks. This will be a topic of future investigation.</p>
<p>This study and others (<xref ref-type="bibr" rid="B7">Dewar et&#xa0;al., 2015</xref>; <xref ref-type="bibr" rid="B20">Gula et&#xa0;al., 2016</xref>; <xref ref-type="bibr" rid="B56">Wenegrat and Thomas, 2020</xref>; <xref ref-type="bibr" rid="B59">Yankovsky et&#xa0;al., 2021</xref>) are strong support that traditionally surface-associated submesoscale frontal instabilities can arise below the SBL when forced by topography; and if parameterized in ocean models, should be treated as more than just an SBL effect. Our results suggest SI below the SBL is ubiquitous in topographically sheared frontal regions, indicating that subsurface parameterization (e.g., <xref ref-type="bibr" rid="B59">Yankovsky et&#xa0;al., 2021</xref>) is useful in regions with complex topography. This said, we emphasize that the presence of unstable flow does not guarantee that SI or its hybrid types will grow on a meaningful timescale or produce a TKE contribution (<xref ref-type="bibr" rid="B13">Ferris and Gong, 2024</xref>). An open task is to estimate the mixing efficiency associated with topographically forced submesoscale instability (<xref ref-type="bibr" rid="B23">Ijichi et&#xa0;al., 2020</xref>), and its relative role (if any) in driving upper ocean structure. The community&#x2019;s need to develop realistic parameterizations for unresolved submesoscale instability is strong motivation to make further observations in regions suspected of topographically-sheared SI, CSI, and CI; and to better understand the growth rates, depths, and re-stratification timescales associated with these instabilities in the real ocean. At the same time, equal focus should be placed on classic shear turbulence and internal wave phenomena in the Southern Ocean, which are likely as important (if not more important) than submesoscale instability away from boundaries.</p>
</sec>
</body>
<back>
<sec id="s5" sec-type="data-availability">
<title>Data availability statement</title>
<p>ROMS model output is archived with William &amp; Mary Scholar Works (<uri xlink:href="https://doi.org/10.25773/8wqm-7r04">https://doi.org/10.25773/8wqm-7r04</uri>). Operational Mercator used for the ROMS (<uri xlink:href="https://github.com/myroms">https://github.com/myroms</uri>) model is made freely available by the EU Copernicus Marine Service (<uri xlink:href="https://marine.copernicus.eu/">https://marine.copernicus.eu/</uri>).</p></sec>
<sec id="s6" sec-type="author-contributions">
<title>Author contributions</title>
<p>LF: Methodology, Writing &#x2013; original draft, Conceptualization. DG: Supervision, Writing &#x2013; review &amp; editing. JK: Writing &#x2013; review &amp; editing, Methodology.</p></sec>
<ack>
<title>Acknowledgments</title>
<p>AUSSOM microstructure data is used courtesy of Louis St. Laurent and was supported by the OCE Division of the National Science Foundation, award 1558639 (PIs St. Laurent and Sophia Merrifield). ROMS output is used courtesy of Harper Simmons and John Pender, for which computational resources were provided by Research Computing Systems at University of Alaska Fairbanks. We thank the VIMS Ocean-Atmosphere &amp; Climate Change Research Fund (Emeritus John Boon) for his gift of a computer. We thank Justin Shapiro and Thilo Klenz for sharing technical expertise.</p>
</ack>
<sec id="s8" sec-type="COI-statement">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
<p>The author(s) declared that they were an editorial board member of Frontiers, at the time of submission. This had no impact on the peer review process and the final decision.</p></sec>
<sec id="s9" sec-type="ai-statement">
<title>Generative AI statement</title>
<p>The author(s) declare that no Generative AI was used in the creation of this manuscript.</p>
<p>Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If&#xa0;you identify any issues, please contact us.</p></sec>
<sec id="s10" sec-type="disclaimer">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p></sec>
<sec id="s11" sec-type="supplementary-material">
<title>Supplementary material</title>
<p>The Supplementary Material for this article can be found online at: <ext-link ext-link-type="uri" xlink:href="https://www.frontiersin.org/articles/10.3389/fmars.2025.1612637/full#supplementary-material">https://www.frontiersin.org/articles/10.3389/fmars.2025.1612637/full#supplementary-material</ext-link></p>
<supplementary-material xlink:href="Image1.jpg" id="SF1" mimetype="image/jpeg"><label>Supplementary Figure&#xa0;1</label>
<caption>
<p>Cross-sections of an idealized jet for the near-boundary case. Nodes satisfying criteria (<xref ref-type="table" rid="T1"><bold>Table&#xa0;1</bold></xref>) for centrifugal (green) and centrifugal-symmetric instability (red) are highlighted (F). There are no instances of pure symmetric instability.</p>
</caption></supplementary-material>
<supplementary-material xlink:href="Image2.jpg" id="SF2" mimetype="image/jpeg"><label>Supplementary Figure&#xa0;2</label>
<caption>
<p>Cross-sections of an idealized jet for the near-boundary case. As in <xref ref-type="supplementary-material" rid="SF1"><bold>Supplementary Figure A1</bold></xref>, nodes satisfying criteria (<xref ref-type="table" rid="T1"><bold>Table&#xa0;1</bold></xref>) for centrifugal (green) and centrifugal-symmetric instability (red) are highlighted (f). There are no instances of pure symmetric instability.</p>
</caption></supplementary-material></sec>
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<app id="app1">
<title>Appendix</title>
<p>We validate the results of the 1-km ROMS hindcast using velocity-based feature model after (<xref ref-type="bibr" rid="B17">Gangopadhyay and Robinson, 2002</xref>). A 2D idealized model (<xref ref-type="supplementary-material" rid="SF1"><bold>Table A1</bold></xref>), based on a PF-associated jet observed during AUSSOM, was created from the geometry observed via AVISO, wind conditions from CCMP V2.0, and approximate density from the glider to investigate the development of instability. The model is a cross-section of a geostrophic zonal jet with no time evolution. The background density structure (&#x3c1;<sub>&#x3b8;</sub>) based on a Drake Passage width of <italic>L<sub>DP</sub></italic> = 850 km and potential density anomaly (<inline-formula>
<mml:math display="inline" id="im11"><mml:mrow><mml:mi>&#x3b4;</mml:mi><mml:msub><mml:mi>&#x3c1;</mml:mi><mml:mi>&#x3b8;</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) which produce the geostrophic jet are given by (<xref ref-type="disp-formula" rid="eqA1b">Equation A1a, A1b</xref>):</p>
<disp-formula id="eqA1a"><label>(A1a)</label>
<mml:math display="block" id="M3"><mml:mrow><mml:msub><mml:mi>&#x3c1;</mml:mi><mml:mi>&#x3b8;</mml:mi></mml:msub><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>z</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>z</mml:mi><mml:msub><mml:mi>r</mml:mi><mml:mi>z</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:mi>y</mml:mi><mml:msub><mml:mi>r</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>&#x3b4;</mml:mi><mml:msub><mml:mi>&#x3c1;</mml:mi><mml:mi>&#x3b8;</mml:mi></mml:msub></mml:mrow></mml:math>
</disp-formula>
<disp-formula id="eqA1b"><label>(A1b)</label>
<mml:math display="block" id="M4"><mml:mrow><mml:mi>&#x3b4;</mml:mi><mml:msub><mml:mi>&#x3c1;</mml:mi><mml:mi>&#x3b8;</mml:mi></mml:msub><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>z</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mn>0.06</mml:mn><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>z</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>H</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mi>tanh</mml:mi><mml:mo>&#xa0;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>y</mml:mi><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mi>&#x3c1;</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo stretchy="false">/</mml:mo><mml:mtext>&#x394;</mml:mtext><mml:msub><mml:mi>y</mml:mi><mml:mi>&#x3c1;</mml:mi></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>
</disp-formula>
<p>where <inline-formula>
<mml:math display="inline" id="im12"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>z</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">/</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>H</mml:mi><mml:msub><mml:mi>&#x3c1;</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> and <inline-formula>
<mml:math display="inline" id="im13"><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mn>0.3</mml:mn><mml:mo stretchy="false">/</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mi>D</mml:mi><mml:mi mathvariant="italic">P</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:msub><mml:mi mathvariant="italic">&#x3c1;</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> and width of the anomaly (&#x394;<italic>y</italic><sub><italic>&#x3c1;</italic></sub>) is 7 km, resulting in stratification <italic>N</italic><sup>2</sup> = 3 &#xd7; 10<sup>&#x2212;6</sup>s<sup>&#x2212;2</sup>. The latitude of the density anomaly <inline-formula>
<mml:math display="inline" id="im14"><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mi>&#x3c1;</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></inline-formula> is chosen to be 100 km (Case Ocean, representing an open ocean jet) or 170 km (Case Boundary, representing near-boundary jet). The jet velocity (<italic>U</italic><sub>0</sub> &#x2264; 1.37 m/s) is calculated using thermal wind balance <inline-formula>
<mml:math display="inline" id="im15"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mi>z</mml:mi></mml:msub><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>z</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub><mml:mo stretchy="false">/</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:math></inline-formula>, where <inline-formula>
<mml:math display="inline" id="im16"><mml:mrow><mml:mi>B</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>z</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mi>g</mml:mi><mml:mi>&#x3c1;</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:msub><mml:mi>&#x3c1;</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> and subscripts indicate differentiated quantities. A horizontal velocity anomaly &#x3b4;U &#x2265; &#x2212;0.35 m/s (<xref ref-type="disp-formula" rid="eqA2b">Equation A2b</xref>) and logarithmic decay function are used to represent the effects of topographic shearing (<xref ref-type="disp-formula" rid="eqA2b">Equation A2c</xref>). The horizontal velocity anomaly is equivalent to representing the effects of a topographic form drag using the expression for wall vorticity, <inline-formula>
<mml:math display="inline" id="im17"><mml:mrow><mml:mi>&#x3b6;</mml:mi><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>&#x3c4;</mml:mi><mml:mi>D</mml:mi></mml:msub><mml:mo stretchy="false">/</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mi>&#x3c1;</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:msub><mml:mi>&#x3bd;</mml:mi><mml:mi>h</mml:mi></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>C</mml:mi><mml:mi>D</mml:mi></mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mo>|</mml:mo><mml:mi>U</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>.</p>
<p>The physical presence of topographic shearing along Namuncur&#xe1; - Burwood Bank is supported by two datasets: (a) a weak westward flow 0.1-0.2 m/s was observed in the 2020 reoccupation of GO-SHIP sections SR1B and A23 across the Drake Passage and Scotia Sea (<xref ref-type="bibr" rid="B16">Firing, 2020</xref>), and (b) a westward velocity anomaly (intermittently amounting to a westward flow, e.g. <xref ref-type="fig" rid="f3"><bold>Figure&#xa0;3b</bold></xref>) of similar magnitude arises in our ROMS model.</p>
<disp-formula id="eqA2a"><label>(A2a)</label>
<mml:math display="block" id="M5"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>z</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mi>U</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>z</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mtext>&#x394;</mml:mtext><mml:mi>z</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>U</mml:mi><mml:mi>z</mml:mi></mml:msub><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>z</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mtext>&#x394;</mml:mtext><mml:mi>z</mml:mi></mml:mrow></mml:math>
</disp-formula>
<disp-formula id="eqA2b"><label>(A2b)</label>
<mml:math display="block" id="M6"><mml:mrow><mml:mi>&#x3b4;</mml:mi><mml:mi>U</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>z</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mo>&#x2212;</mml:mo><mml:mn>0.35</mml:mn><mml:mi>tanh</mml:mi><mml:mo>&#xa0;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>y</mml:mi><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:msub><mml:mn>0</mml:mn><mml:mi>U</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo stretchy="false">/</mml:mo><mml:mtext>&#x394;</mml:mtext><mml:msub><mml:mi>y</mml:mi><mml:mi>U</mml:mi></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>
</disp-formula>
<disp-formula id="eqA2c"><label>(A2c)</label>
<mml:math display="block" id="M7"><mml:mrow><mml:mi>U</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>z</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mrow><mml:mtable columnalign="left"><mml:mtr columnalign="left"><mml:mtd columnalign="left"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mi>&#x3b4;</mml:mi><mml:mi>U</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:mtd><mml:mtd columnalign="left"><mml:mrow><mml:mtext>if</mml:mtext><mml:mtext>&#x2009;</mml:mtext><mml:mi>y</mml:mi><mml:mo>&#x2264;</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:msub><mml:mn>0</mml:mn><mml:mi>U</mml:mi></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:mtd></mml:mtr><mml:mtr columnalign="left"><mml:mtd columnalign="left"><mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mi>&#x3b4;</mml:mi><mml:mi>U</mml:mi></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mfrac><mml:mrow><mml:mi>ln</mml:mi><mml:mo>&#xa0;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>L</mml:mi><mml:mo>&#x2212;</mml:mo><mml:mi>y</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>ln</mml:mi><mml:mo>&#xa0;</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>L</mml:mi><mml:mo>&#x2212;</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:msub><mml:mn>0</mml:mn><mml:mi>U</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac><mml:mo>,</mml:mo></mml:mrow></mml:mtd><mml:mtd columnalign="left"><mml:mrow><mml:mtext>if</mml:mtext><mml:mtext>&#x2009;</mml:mtext><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:msub><mml:mn>0</mml:mn><mml:mi>U</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>&lt;</mml:mo><mml:mi>y</mml:mi></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:mrow></mml:mrow></mml:math>
</disp-formula>
<p>Here (<xref ref-type="disp-formula" rid="eqA2b">Equation A2b, A2c</xref>) <inline-formula>
<mml:math display="inline" id="im18"><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mrow><mml:msub><mml:mn>0</mml:mn><mml:mi>U</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>170</mml:mn><mml:mo>&#xa0;</mml:mo><mml:mtext>km</mml:mtext></mml:mrow></mml:math></inline-formula> and &#x394;<italic>y<sub>U</sub></italic> = 3 km. Omitting the topographic boundary layer, the transport is similar for both idealized scenarios; 30.73 Sv for Case Ocean and 30.87 Sv for Case Boundary.</p>
<p>Cross-sections of the jet in both cases are provided (<xref ref-type="supplementary-material" rid="SF1"><bold>Supplementary Figures A1</bold></xref>, <xref ref-type="supplementary-material" rid="SF2"><bold>A2</bold></xref>) with instabilities (<xref ref-type="table" rid="T1"><bold>Table&#xa0;1</bold></xref>) highlighted over Ertel potential vorticity. In Case Ocean (<xref ref-type="supplementary-material" rid="SF1"><bold>Supplementary Figure A1</bold></xref>), stratification effects create CSI which doubles the total amount of overturning instability that would otherwise be limited to CI. In Case Boundary (<xref ref-type="supplementary-material" rid="SF1"><bold>Supplementary Figure A2</bold></xref>), close proximity of the jet to the northern boundary increases the instances of CI, which is augmented by a doubling in CSI. The CSI extends throughout the water column, illustrating it is not a process specific to the surface ocean as commonly intuited. This feature model validates the conclusion derived from the ROMS model, that an otherwise identical jet can produce different amounts of subsurface submesoscale instability depending on its location relative to topography.</p>
<table-wrap id="TA1" position="float">
<label>Table&#xa0;A1</label>
<caption>
<p>Parameters for 2D model.</p>
</caption>
<table frame="hsides">
<tbody>
<tr>
<td valign="top" align="left">Domain height</td>
<td valign="top" align="left"><italic>H</italic> = 3000 m</td>
</tr>
<tr>
<td valign="top" align="left">Domain weight</td>
<td valign="top" align="left"><italic>L</italic> = 200 km</td>
</tr>
<tr>
<td valign="top" align="left">Vertical grid divisions</td>
<td valign="top" align="left"><italic>NZ</italic> = 51 (&#x394;<italic>z</italic> &#x2248; 60 m)</td>
</tr>
<tr>
<td valign="top" align="left">Horizontal grid divisions</td>
<td valign="top" align="left"><italic>NY</italic> = 301 (&#x394;<italic>y</italic> &#x2248; 0.67 km)</td>
</tr>
<tr>
<td valign="top" align="left">Base latitude</td>
<td valign="top" align="left">57&#xb0;S</td>
</tr>
<tr>
<td valign="top" align="left">Reference density</td>
<td valign="top" align="left"><italic>&#x3c1;</italic><sub>0</sub> = 1027 kg/m<sup>3</sup></td>
</tr>
</tbody>
</table>
</table-wrap>
</app>
</app-group>
<fn-group>
<fn id="n1" fn-type="custom" custom-type="edited-by">
<p>Edited by: <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1143992">Anna Oliv&#xe9; Abell&#xf3;</ext-link>, Spanish National Research Council (CSIC), Spain</p></fn>
<fn id="n2" fn-type="custom" custom-type="reviewed-by">
<p>Reviewed by: <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1760076">Tien Anh Tran</ext-link>, Seoul National University, Republic of Korea; <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3046731">Christopher Auckland</ext-link>, University of East Anglia, United Kingdom</p></fn>
</fn-group>
</back>
</article>