<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" "https://jats.nlm.nih.gov/nlm-dtd/publishing/3.0/journalpublishing3.dtd">
<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" article-type="research-article" dtd-version="3.0" xml:lang="en">
<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-6-997-2010</article-id>
<title-group>
<article-title>Retroflection from a double-slanted coastline: a model for the Agulhas leakage variability</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Zharkov</surname>
<given-names>V.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Nof</surname>
<given-names>D.</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Weijer</surname>
<given-names>W.</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
</contrib>
</contrib-group><aff id="aff1">
<label>1</label>
<addr-line>Geophysical Fluid Dynamics Institute, Florida State University, Tallahassee, FL, 32306, USA</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>Department of Oceanography, Florida State University, Tallahassee, FL, 32306, USA</addr-line>
</aff>
<aff id="aff3">
<label>3</label>
<addr-line>New Mexico Consortium, Los Alamos National Laboratory, Los Alamos, NM 87545, USA</addr-line>
</aff>
<pub-date pub-type="epub">
<day>13</day>
<month>12</month>
<year>2010</year>
</pub-date>
<volume>6</volume>
<issue>4</issue>
<fpage>997</fpage>
<lpage>1011</lpage>
<permissions>
<copyright-statement>Copyright: &#x000a9; 2010 V. Zharkov et al.</copyright-statement>
<copyright-year>2010</copyright-year>
<license license-type="open-access">
<license-p>This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit <ext-link ext-link-type="uri"  xlink:href="https://creativecommons.org/licenses/by/3.0/">https://creativecommons.org/licenses/by/3.0/</ext-link></license-p>
</license>
</permissions>
<self-uri xlink:href="https://os.copernicus.org/articles/6/997/2010/os-6-997-2010.html">This article is available from https://os.copernicus.org/articles/6/997/2010/os-6-997-2010.html</self-uri>
<self-uri xlink:href="https://os.copernicus.org/articles/6/997/2010/os-6-997-2010.pdf">The full text article is available as a PDF file from https://os.copernicus.org/articles/6/997/2010/os-6-997-2010.pdf</self-uri>
<abstract>
<p>The Agulhas leakage to the South Atlantic exhibits a strong anti-correlation
with the mass flux of the Agulhas Current. When the Agulhas retroflection is
in its normal position near Cape Agulhas, leakage is relatively high and the
nearby South African coastal slant (angle of derivation from zonal) is very
small and relatively invariant alongshore. During periods of strong incoming
flux (low leakage), the retroflection shifts upstream to Port Elizabeth or
East London, where the coastline shape has a &quot;kink&quot;, i.e., the slant
changes abruptly from small on the west side, to large (about 55°) on
the east side. Here, we show that the variability of rings shedding and
anti-correlation between Agulhas mass flux and leakage to the South Atlantic
may be attributed to this kink.
&lt;br&gt;&lt;br&gt;
To do so, we develop a nonlinear analytical model for retroflection near a
coastline that consists of two sections, a zonal western section and a
strongly slanted eastern section. The principal difference between this and
the model of a straight slanted coast (discussed in our earlier papers)
is that, here, free purely westward propagation of eddies along the zonal
coastline section is allowed. This introduces an interesting situation in
which strong slant of the coast east of the kink prohibits the formation and
shedding of rings, while the almost zonal coastal orientation west of the
kink encourages shedding. Therefore, the kink &quot;locks&quot; the position of the
retroflection, forcing it to occur just downstream of the kink. Rings are
necessarily shed from the retroflection area in our kinked model, regardless
of the degree of eastern coast slant. In contrast, a no-kink model with a
coastline of intermediate slant indicates that shedding is almost completely
arrested by that slant.
&lt;br&gt;&lt;br&gt;
We suggest that the observed difference in ring-shedding intensity during
times of normal retroflection position and times when the retroflection is
shifted eastward is due to the change in the retroflection location with
respect to the kink. When the incoming flux detaches from the coast north of
the kink, ring transport is small; when the flux detaches south of the kink,
transport is large. Simple process-oriented numerical simulations are in
fair agreement with our analytical results.</p>
</abstract>
<counts><page-count count="15"/></counts>
</article-meta>
</front>
<body/>
<back>
<ref-list>
<title>References</title>
<ref id="ref1">
<label>1</label><mixed-citation publication-type="other" xlink:type="simple">Arruda, W. Z., Nof, D., and O&apos;Brien, J. J.: Does the Ulleung eddy owe its existence to &lt;i&gt;β&lt;/i&gt; and nonlinearities?, Deep-Sea Res., 51, 2073–2090, 2004.</mixed-citation>
</ref>
<ref id="ref2">
<label>2</label><mixed-citation publication-type="other" xlink:type="simple">Biastoch, A., Böning, C. W., and Lutjeharms, J. R. E.: Agulhas leakage dynamics affects decadal variability in Atlantic overturning circulation, Nature, 456, 489–492, 2008.</mixed-citation>
</ref>
<ref id="ref3">
<label>3</label><mixed-citation publication-type="other" xlink:type="simple">Bleck, R. and Boudra, D.: Wind-driven spin-up in eddy-resolving ocean models formulated in isopycnic and isobaric coordinates, J. Geophys. Res., 91, 7611–7621, 1986.</mixed-citation>
</ref>
<ref id="ref4">
<label>4</label><mixed-citation publication-type="other" xlink:type="simple">Boudra, D. B. and Chassignet, E. P.: Dynamics of the Agulhas retroflection and ring formation in a numerical model, I. The vorticity balance, J. Phys. Oceanogr., 18, 280–303, 1988.</mixed-citation>
</ref>
<ref id="ref5">
<label>5</label><mixed-citation publication-type="other" xlink:type="simple">Byrne, A. D., Gordon, A. L., and Haxby, W. F.: Agulhas eddies: A synoptic view using Geosat ERM data, J. Phys. Oceanogr., 25, 902–917, 1995.</mixed-citation>
</ref>
<ref id="ref6">
<label>6</label><mixed-citation publication-type="other" xlink:type="simple">Chassignet, E. P. and Boudra, D. B.: Dynamics of the Agulhas retroflection and ring formation in a numerical model, II. Energetics and ring formation, J. Phys. Oceanogr., 18, 304–319, 1988.</mixed-citation>
</ref>
<ref id="ref7">
<label>7</label><mixed-citation publication-type="other" xlink:type="simple">De Ruijter, W. P. M.: Asymptotic analysis of the Agulhas and Brazil Current systems, J. Phys. Oceanogr., 12, 361–373, 1982.</mixed-citation>
</ref>
<ref id="ref8">
<label>8</label><mixed-citation publication-type="other" xlink:type="simple">De Ruijter, W. P. M. and Boudra, D. B.: The wind-driven circulation in the South Atlantic – Indian Ocean, I. Numerical experiments in a one-layer model, Deep-Sea Res., 32, 557–574, 1985.</mixed-citation>
</ref>
<ref id="ref9">
<label>9</label><mixed-citation publication-type="other" xlink:type="simple">De Ruijter, W. P. M., Biastoch, A., Drijfhout, S. S., Lutjeharms, J. R. E., Matano, R. P., Pichevin, T., Van Leeuwen, P. J., and Weijer, W.: Indian Atlantic interocean exchange: Dynamics, estimation and impact, J. Geophys. Res., 104, 20885–20910, 1999.</mixed-citation>
</ref>
<ref id="ref10">
<label>10</label><mixed-citation publication-type="other" xlink:type="simple">De Ruijter, W. P. M., Van Aken, H. M., Beier, E. J., Lutjeharms, J. R. E., Matano, R. P., and Schouten, M. W.: Eddies and dipoles around South Madagascar: formation, pathways and large-scale impact, Deep-Sea Res., 51, 383–400, 2004.</mixed-citation>
</ref>
<ref id="ref11">
<label>11</label><mixed-citation publication-type="other" xlink:type="simple">Doglioli, A. M., Veneziani, M., Blanke, B., Speich, S., and Grifta, A.: A Lagrangian analysis of the Indian Atlantic interocean exchange in a regional model, Geophys. Res. Lett., 33, L14611, https://doi.org/10.1029/2006GL026498, 2006.</mixed-citation>
</ref>
<ref id="ref12">
<label>12</label><mixed-citation publication-type="other" xlink:type="simple">Esper, O., Versteegh, G. J. M., Zonneveld, K. A. F., and Willems, H.: A palynological reconstruction of the Agulhas Retroflection (South Atlantic Ocean) during the Late Quaternary, Global Planet. Change, 41, 31–62, 2004.</mixed-citation>
</ref>
<ref id="ref13">
<label>13</label><mixed-citation publication-type="other" xlink:type="simple">Ffield, A., Toole, J., and Wilson, D.: Seasonal circulation in the South Indian Ocean, Geophys. Res. Lett., 24, 2773–2776, 1997.</mixed-citation>
</ref>
<ref id="ref14">
<label>14</label><mixed-citation publication-type="other" xlink:type="simple">Goni, G. J., Garzoli, S. L. Roubicek, A. J., Olson, D. B., and Brown, O. B.: Agulhas ring dynamics from TOPEX/POSEIDON satellite altimeter data, J. Mar. Res., 55, 861–883, 1997.</mixed-citation>
</ref>
<ref id="ref15">
<label>15</label><mixed-citation publication-type="other" xlink:type="simple">Gordon, A. L., Lutjeharms, J. R. E., and Gründlingh, M. L.: Stratification and circulation at the Agulhas Retroflection, Deep-Sea Res., 34, 565–599, 1987.</mixed-citation>
</ref>
<ref id="ref16">
<label>16</label><mixed-citation publication-type="other" xlink:type="simple">Lutjeharms, J. R. E.: The Agulhas Current, Springer-Verlag, Berlin-Heidelberg-New York, XIV, 330 pp., 2006.</mixed-citation>
</ref>
<ref id="ref17">
<label>17</label><mixed-citation publication-type="other" xlink:type="simple">Lutjeharms, J. R. E. and Van Ballegooyen, R. C.: Topographic control in the Agulhas Current system, Deep-Sea Res., 31, 1321–1337, 1984.</mixed-citation>
</ref>
<ref id="ref18">
<label>18</label><mixed-citation publication-type="other" xlink:type="simple">Lutjeharms, J. R. E. and Van Ballegooyen, R. C.: The retroflection of the Agulhas Current, J. Phys. Oceanogr., 18, 1570–1583, 1988a.</mixed-citation>
</ref>
<ref id="ref19">
<label>19</label><mixed-citation publication-type="other" xlink:type="simple">Lutjeharms, J. R. E. and Van Ballegooyen, R. C.: Anomalous upstream retroflection in the Agulhas current, Science, 240, 1770–1772, 1988b.</mixed-citation>
</ref>
<ref id="ref20">
<label>20</label><mixed-citation publication-type="other" xlink:type="simple">Matano, R. P., Simionato, C. G., De Ruijter, W. P. M., Van Leeuwen, P. J., Strub, P. T., Chelton, D. B., and Schlax, M. G.: Seasonal variability in the Agulhas Retroflection region, Geophys. Res. Lett., 25, 4361–4364, 1998.</mixed-citation>
</ref>
<ref id="ref21">
<label>21</label><mixed-citation publication-type="other" xlink:type="simple">Nof, D.: On the β-induced movement of isolated baroclinic eddies, J. Phys. Oceanogr., 11, 1662–1672, 1981.</mixed-citation>
</ref>
<ref id="ref22">
<label>22</label><mixed-citation publication-type="other" xlink:type="simple">Nof, D.: On the migration of isolated eddies with application to Gulf stream rings, J. Mar. Res., 31, 399–425, 1983.</mixed-citation>
</ref>
<ref id="ref23">
<label>23</label><mixed-citation publication-type="other" xlink:type="simple">Nof, D.: The momentum imbalance paradox revisited, J. Phys. Oceanogr., 35, 1928–1939, 2005.</mixed-citation>
</ref>
<ref id="ref24">
<label>24</label><mixed-citation publication-type="other" xlink:type="simple">Nof, D. and Pichevin, T.: The retroflection paradox, J. Phys. Oceanogr., 26, 2344–2358, 1996.</mixed-citation>
</ref>
<ref id="ref25">
<label>25</label><mixed-citation publication-type="other" xlink:type="simple">Nof, D. and Pichevin, T.: The ballooning of outflows, J. Phys. Oceanogr., 31, 3045–3058, 2001.</mixed-citation>
</ref>
<ref id="ref26">
<label>26</label><mixed-citation publication-type="other" xlink:type="simple">Orlanski, I.: A simple boundary condition for unbounded hyperbolic flows, J. Comput. Phys., 21, 251–269, 1976.</mixed-citation>
</ref>
<ref id="ref27">
<label>27</label><mixed-citation publication-type="other" xlink:type="simple">Ou, H. W. and De Ruijter, W. P. M.: Separation of an internal boundary current from a curved coast line, J. Phys. Oceanogr., 16, 280–289, 1986.</mixed-citation>
</ref>
<ref id="ref28">
<label>28</label><mixed-citation publication-type="other" xlink:type="simple">Pichevin, T., Nof, D., and Lutjeharms, J. R. E.: Why are there Agulhas Rings? J. Phys. Oceanogr., 29, 693–707, 1999.</mixed-citation>
</ref>
<ref id="ref29">
<label>29</label><mixed-citation publication-type="other" xlink:type="simple">Pichevin, T., Herbette, S., and Floc&apos;h, F.: Eddy formation and shedding in a separating boundary current, J. Phys. Oceanogr., 39, 1921–1934, 2009.</mixed-citation>
</ref>
<ref id="ref30">
<label>30</label><mixed-citation publication-type="other" xlink:type="simple">Quartly, G. D. and Srokosz, M. A.: SST Observations of the Agulhas and East Madagascar Retroflections by the TRMM Microwave Imager, J. Phys. Oceanogr., 32, 1585–1592, 2002.</mixed-citation>
</ref>
<ref id="ref31">
<label>31</label><mixed-citation publication-type="other" xlink:type="simple">Reason, C. J. C., Lutjeharms, J. R. E., Hermes, J., Biastoch, A., and Roman, R. E.: Inter-ocean fluxes south of Africa in an eddy-permitting model, Deep-Sea Res. Pt. II, 50, 281–298, 2003.</mixed-citation>
</ref>
<ref id="ref32">
<label>32</label><mixed-citation publication-type="other" xlink:type="simple">Schouten, M. W., De Ruijter, W. P. M., Van Leeuwen, P. J., and Lutjeharms, J. R. E.: Translation, decay and splitting of Agulhas rings in the south-eastern Atlantic ocean, J. Geophys. Res., 105, 21913–21925, 2000.</mixed-citation>
</ref>
<ref id="ref33">
<label>33</label><mixed-citation publication-type="other" xlink:type="simple">Shannon, L. V.: The Benguela ecosystem: Part I. Evolution of the Benguela, physical features and processes, Oceanogr. Mar. Biol., 23, 105–182, 1985.</mixed-citation>
</ref>
<ref id="ref34">
<label>34</label><mixed-citation publication-type="other" xlink:type="simple">Shannon, L. V., Agenbag, J. J., Walker, N. D., and Lutjeharms, J. R. E.: A major perturbation in the Agulhas retroflection area in 1986, Deep-Sea Res., 37, 493–512, 1990.</mixed-citation>
</ref>
<ref id="ref35">
<label>35</label><mixed-citation publication-type="other" xlink:type="simple">Van Aken, H. M., Van Veldhoven, A. K., Veth, C., De Ruijter, W. P. M., Van Leeuwen, P. J., Drijfhout, S. S., Whittle, C. P., and Rouault, M.: Observations of a young Agulhas ring, Astrid, during MARE in March 2000, Deep-Sea Res., 50, 167–195, 2003.</mixed-citation>
</ref>
<ref id="ref36">
<label>36</label><mixed-citation publication-type="other" xlink:type="simple">Van Sebille, E.: Assessing Agulhas leakage, Proefschrift ter verkrijging van de graad van doctor aan de Universiteit Utrecht, 165 pp., 2009.</mixed-citation>
</ref>
<ref id="ref37">
<label>37</label><mixed-citation publication-type="other" xlink:type="simple">Van Sebille, E., Biastoch, A., Van Leeuwen, P. J., and De Ruijter, W. P. M.: A weaker Agulhas current leads to more Agulhas leakage, Geophys. Res. Lett., 36, L03601, https://doi.org/10.1029/2008GL036614, 2009a.</mixed-citation>
</ref>
<ref id="ref38">
<label>38</label><mixed-citation publication-type="other" xlink:type="simple">Van Sebille, E., Barron, C. N., Biastoch, A., Van Leeuwen, P. J., Vossepoel, F. C., and De Ruijter, W. P. M.: Relating Agulhas leakage to the Agulhas Current retroflection location, Ocean Sci., 5, 511–521, 2009b.</mixed-citation>
</ref>
<ref id="ref39">
<label>39</label><mixed-citation publication-type="other" xlink:type="simple">Van Sebille, E., Van Leeuwen, P. J., Biastoch, A., and De Ruijter, W. P. M.: On the fast decay of Agulhas rings, J. Geophys. Res., 115, C0310, https://doi.org/10.1029/2009JC005585, 2010.</mixed-citation>
</ref>
<ref id="ref40">
<label>40</label><mixed-citation publication-type="other" xlink:type="simple">Weijer, W., De Ruijter, W. P. M., Dijkstra, H. A., and Van Leeuwen, P. J.: Impact of interbasin exchange on the Atlantic Overturning Circulation, J. Phys. Oceanogr., 29, 2266–2284, 1999.</mixed-citation>
</ref>
<ref id="ref41">
<label>41</label><mixed-citation publication-type="other" xlink:type="simple">Weijer, W., De Ruijter, W. P. M., Sterl, A., and Drijfhout, S. S.: Response of the Atlantic overturning circulation to South Atlantic sources of buoyancy, Global Planet. Change, 34, 293–311, 2002.</mixed-citation>
</ref>
<ref id="ref42">
<label>42</label><mixed-citation publication-type="other" xlink:type="simple">Zharkov, V. and Nof, D.: Retroflection from slanted coastlines – circumventing the &quot;vorticity paradox&quot;, Ocean Sci., 4, 293–306, 2008a.</mixed-citation>
</ref>
<ref id="ref43">
<label>43</label><mixed-citation publication-type="other" xlink:type="simple">Zharkov, V. and Nof, D.: Agulhas ring injection into the South Atlantic during glacials and interglacials, Ocean Sci., 4, 223–237, 2008b.</mixed-citation>
</ref>
</ref-list>
</back>
</article>