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<front>
<journal-meta>
<journal-id journal-id-type="publisher">OS</journal-id>
<journal-title-group>
<journal-title>Ocean Science</journal-title>
<abbrev-journal-title abbrev-type="publisher">OS</abbrev-journal-title>
<abbrev-journal-title abbrev-type="nlm-ta">Ocean Sci.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">1812-0792</issn>
<publisher><publisher-name>Copernicus Publications</publisher-name>
<publisher-loc>Göttingen, Germany</publisher-loc>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.5194/os-10-127-2014</article-id>
<title-group>
<article-title>The instability of diffusive convection and its implication for the thermohaline staircases in the deep Arctic Ocean</article-title>
</title-group>
<contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Zhou</surname>
<given-names>S.-Q.</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>Qu</surname>
<given-names>L.</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>Lu</surname>
<given-names>Y.-Z.</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>Song</surname>
<given-names>X.-L.</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-group><aff id="aff1">
<label>1</label>
<addr-line>State Key Laboratory of Tropical Oceanography, South China Sea  Institute of Oceanology, 164 West Xingang Road, Haizhu  District, Guangzhou 510301, China</addr-line>
</aff>
<aff id="aff2">
<label>2</label>
<addr-line>University of Chinese Academy of Sciences, Beijing, 100049, China</addr-line>
</aff>
<pub-date pub-type="epub">
<day>24</day>
<month>02</month>
<year>2014</year>
</pub-date>
<volume>10</volume>
<issue>1</issue>
<fpage>127</fpage>
<lpage>134</lpage>
<permissions>
<copyright-statement>Copyright: &#x000a9; 2014 S.-Q. Zhou et al.</copyright-statement>
<copyright-year>2014</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/10/127/2014/os-10-127-2014.html">This article is available from https://os.copernicus.org/articles/10/127/2014/os-10-127-2014.html</self-uri>
<self-uri xlink:href="https://os.copernicus.org/articles/10/127/2014/os-10-127-2014.pdf">The full text article is available as a PDF file from https://os.copernicus.org/articles/10/127/2014/os-10-127-2014.pdf</self-uri>
<abstract>
<p>In the present study, the classical description of diffusive convection is
updated to interpret the instability of diffusive interfaces and the
dynamical evolution of the bottom layer in the deep Arctic Ocean. In the new
consideration of convective instability, both the background salinity
stratification and rotation are involved. The critical Rayleigh number of
diffusive convection is found to vary from 10&lt;sup&gt;3&lt;/sup&gt; to 10&lt;sup&gt;11&lt;/sup&gt; in the deep
Arctic Ocean as well as in other oceans and lakes. In such a wide range of
conditions, the interface-induced thermal Rayleigh number is shown to be
consistent with the critical Rayleigh number of diffusive convection. In most
regions, background salinity stratification is found to be the main hindrance
to the occurrence of convecting layers. With the new parameterization, it is
predicted that the maximum thickness of the bottom layer is 1051 m in the
deep Arctic Ocean, which is close to the observed value of 929 m. The evolution time of
the bottom layer is predicted to be ~ 100 yr, which is on the same
order as that based on &lt;sup&gt;14&lt;/sup&gt;C isolation age estimation.</p>
</abstract>
<counts><page-count count="8"/></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">Anschutz, P. and Blanc, G.: Heat and salt fluxes in the Atlantis II Deep (Red Sea), Earth Planet. Sc. Lett, 142, 147–159, &lt;a href=&quot;http://dx.doi.org/10.1016/0012-821X(96)00098-2&quot;&gt;https://doi.org/10.1016/0012-821X(96)00098-2&lt;/a&gt;, 1996.</mixed-citation>
</ref>
<ref id="ref2">
<label>2</label><mixed-citation publication-type="other" xlink:type="simple">BGOS: The hydrographic data measured by the Ice-Tethered Profiler 2 (ITP2) in Beaufort Gyre Observing System (BGOS) were used in the present work, available at: &lt;a href=&quot;http://www.whoi.edu/itp&quot;&gt;http://www.whoi.edu/itp&lt;/a&gt; (last access: 20 February 2014), 2013.</mixed-citation>
</ref>
<ref id="ref3">
<label>3</label><mixed-citation publication-type="other" xlink:type="simple">Björk, G. and Winsor, P.: The deep waters of the Eurasian Basin, Arctic Ocean: Geothermal heat flow, mixing and renewal, Deep Sea Res.-Pt. I, 53, 1253–1271, &lt;a href=&quot;http://dx.doi.org/10.1016/j.dsr.2006.05.006&quot;&gt;https://doi.org/10.1016/j.dsr.2006.05.006&lt;/a&gt;, 2006.</mixed-citation>
</ref>
<ref id="ref4">
<label>4</label><mixed-citation publication-type="other" xlink:type="simple">Caldwell, D. R.: Experimental studies on the onset of thermohaline convection, J. Fluid Mech., 64, 347–368, &lt;a href=&quot;http://dx.doi.org/10.1017/S0022112074002436&quot;&gt;https://doi.org/10.1017/S0022112074002436&lt;/a&gt;, 1974.</mixed-citation>
</ref>
<ref id="ref5">
<label>5</label><mixed-citation publication-type="other" xlink:type="simple">Carmack, E. C., Williams, W. J., Zimmermann, S. L., and McLaughlin, F. A.: The Arctic Ocean warms from below, J. Geophys. Res., 39, L07604, &lt;a href=&quot;http://dx.doi.org/10.1029/2012GL050890&quot;&gt;https://doi.org/10.1029/2012GL050890&lt;/a&gt;, 2012.</mixed-citation>
</ref>
<ref id="ref6">
<label>6</label><mixed-citation publication-type="other" xlink:type="simple">Carpenter, J. R., Sommer, T., and Wuest, A.: Stability of a double-diffusive interface in the diffusive convection regime, J. Phys. Oceanogr., 42, 840–854, &lt;a href=&quot;http://dx.doi.org/10.1175/JPO-D-11-0118.1&quot;&gt;https://doi.org/10.1175/JPO-D-11-0118.1&lt;/a&gt;, 2012.</mixed-citation>
</ref>
<ref id="ref7">
<label>7</label><mixed-citation publication-type="other" xlink:type="simple">Castaing, B., Gunaratne, G., Heslot, F., Kadanoff, L., Libchaber, A., Thomae, S., Wu, X.-Z., Zaleski, S., and Zanetti, G.: Scaling of hard thermal turbulence in Rayleigh-Bénard convection, J. Fluid Mech., 204, 1–30, &lt;a href=&quot;http://dx.doi.org/10.1017/S0022112089001643&quot;&gt;https://doi.org/10.1017/S0022112089001643&lt;/a&gt;, 1989.</mixed-citation>
</ref>
<ref id="ref8">
<label>8</label><mixed-citation publication-type="other" xlink:type="simple">Fernando, H. J. S.: The formation of layered structure when a stable salinity gradient is heated from below, J. Fluid Mech., 182, 525–541, &lt;a href=&quot;http://dx.doi.org/10.1017/S0022112087002441&quot;&gt;https://doi.org/10.1017/S0022112087002441&lt;/a&gt;, 1987.</mixed-citation>
</ref>
<ref id="ref9">
<label>9</label><mixed-citation publication-type="other" xlink:type="simple">Frisch, U.: Turbulence: the Legacy of A. N. Kolmogorov, Cambridge University Press, UK, 1995.</mixed-citation>
</ref>
<ref id="ref10">
<label>10</label><mixed-citation publication-type="other" xlink:type="simple">Howard, L. N.: Convection at high Rayleigh number, Proc. 11th Cong. Applied Mech., edited by: Grtler, H., 1964.</mixed-citation>
</ref>
<ref id="ref11">
<label>11</label><mixed-citation publication-type="other" xlink:type="simple">Huppert, H. E. and Linden, P. F.: On heating a stable salinity gradient from below, J. Fluid Mech., 95, 431–464, &lt;a href=&quot;http://dx.doi.org/10.1017/S0022112079001543&quot;&gt;https://doi.org/10.1017/S0022112079001543&lt;/a&gt;, 1979.</mixed-citation>
</ref>
<ref id="ref12">
<label>12</label><mixed-citation publication-type="other" xlink:type="simple">Huppert, H. E. and Moore, D. R.: Nonlinear double-diffusive convection, J. Fluid Mech., 78, 821–854, &lt;a href=&quot;http://dx.doi.org/10.1017/S0022112076002759&quot;&gt;https://doi.org/10.1017/S0022112076002759&lt;/a&gt;, 1976.</mixed-citation>
</ref>
<ref id="ref13">
<label>13</label><mixed-citation publication-type="other" xlink:type="simple">Kelley, D. E., Fernando, H. J. S., Gargett, A. E., Tanny, J., and Özsoy, E.: The diffusive regime of double diffusive convection, Progr. Oceanogr., 56, 461–481, &lt;a href=&quot;http://dx.doi.org/10.1016/S0079-6611(03)00026-0&quot;&gt;https://doi.org/10.1016/S0079-6611(03)00026-0&lt;/a&gt;, 2003.</mixed-citation>
</ref>
<ref id="ref14">
<label>14</label><mixed-citation publication-type="other" xlink:type="simple">Langseth, M. G., Lachenbruch, A., and Marshall, V. B.: Geothermal observations in the Arctic region, The Geology of North America: the Arctic Ocean region, The Geological Society of America, 1990.</mixed-citation>
</ref>
<ref id="ref15">
<label>15</label><mixed-citation publication-type="other" xlink:type="simple">Larson, N. G. and Gregg, M. C.: Turbulent dissipation and shear in thennohaline intrusions, Nature, 306, 26–32, &lt;a href=&quot;http://dx.doi.org/10.1038/306026a0&quot;&gt;https://doi.org/10.1038/306026a0&lt;/a&gt;, 1983.</mixed-citation>
</ref>
<ref id="ref16">
<label>16</label><mixed-citation publication-type="other" xlink:type="simple">Linden, P. F. and Shirtcliffe, T. G. L.: The diffusive interface in double-diffusive convection, J. Fluid Mech., 87, 417–432, &lt;a href=&quot;http://dx.doi.org/10.1017/S002211207800169X&quot;&gt;https://doi.org/10.1017/S002211207800169X&lt;/a&gt;, 1978.</mixed-citation>
</ref>
<ref id="ref17">
<label>17</label><mixed-citation publication-type="other" xlink:type="simple">Lui, S. L. and Xia, K. Q.: Spatial structure of the thermal boundary layer in turbulent convection, Phys. Rev. E, 57, 5494–5503, &lt;a href=&quot;http://dx.doi.org/10.1103/PhysRevE.57.5494&quot;&gt;https://doi.org/10.1103/PhysRevE.57.5494&lt;/a&gt;, 1998.</mixed-citation>
</ref>
<ref id="ref18">
<label>18</label><mixed-citation publication-type="other" xlink:type="simple">Macdonald, R., Carmack, E. C., and Wallace, D. W. R.: Tritium and radiocarbon dating of Canada basin deep waters, Science, 259, 103–104, &lt;a href=&quot;http://dx.doi.org/10.1126/science.259.5091.103&quot;&gt;https://doi.org/10.1126/science.259.5091.103&lt;/a&gt;, 1993.</mixed-citation>
</ref>
<ref id="ref19">
<label>19</label><mixed-citation publication-type="other" xlink:type="simple">Ostrom, W., Kemp, J., Krishfield, R., and Proshutinsky, A.: Beaufort Gyre freshwater experiment: Deployment operations and technology in 2003, Technical Report WHOI-2004-1, Woods Hole Oceanographic Institution, 2004.</mixed-citation>
</ref>
<ref id="ref20">
<label>20</label><mixed-citation publication-type="other" xlink:type="simple">Padman, L. and Dillon, T. M.: Vertical heat fluxes through the Beaufort Sea thermohaline staircase, J. Geophys. Res., 92, 10799–10806, &lt;a href=&quot;http://dx.doi.org/10.1029/JC092iC10p10799&quot;&gt;https://doi.org/10.1029/JC092iC10p10799&lt;/a&gt;, 1987.</mixed-citation>
</ref>
<ref id="ref21">
<label>21</label><mixed-citation publication-type="other" xlink:type="simple">Padman, L. and Dillon, T. M.: Thermal microstructure and internal waves in the Canada Basin diffusive staircase, Deep Sea Res.-Pt. I, 36, 531–542, &lt;a href=&quot;http://dx.doi.org/10.1016/0198-0149(89)90004-6&quot;&gt;https://doi.org/10.1016/0198-0149(89)90004-6&lt;/a&gt;, 1989.</mixed-citation>
</ref>
<ref id="ref22">
<label>22</label><mixed-citation publication-type="other" xlink:type="simple">Pearlstein, A. J.: Effect of rotation on the stability of a doubly diffusive fluid layer, J. Fluid Mech., 103, 389–412, &lt;a href=&quot;http://dx.doi.org/10.1017/S0022112081001390&quot;&gt;https://doi.org/10.1017/S0022112081001390&lt;/a&gt;, 1981.</mixed-citation>
</ref>
<ref id="ref23">
<label>23</label><mixed-citation publication-type="other" xlink:type="simple">Proshutinsky, A., Krishfield, R., Timmermans, M.-L., Toole, J., Carmack, E., McLaughlin, F., Williams, W. J., Zimmermann, S., Itoh, M., and Shimada, K.: Beaufort Gyre freshwater reservoir: State and variability from observations, J. Geophys. Res., 114, C00A10, &lt;a href=&quot;http://dx.doi.org/10.1029/2008JC005104&quot;&gt;https://doi.org/10.1029/2008JC005104&lt;/a&gt;, 2009.</mixed-citation>
</ref>
<ref id="ref24">
<label>24</label><mixed-citation publication-type="other" xlink:type="simple">Sánchez, X. and Roget, E.: Microstructure measurements and heat flux calculations of a triple-diffusive process in a lake within the diffusive layer convection regime, J. Geophys. Res., 112, C02012, &lt;a href=&quot;http://dx.doi.org/10.1029/2006JC003750&quot;&gt;https://doi.org/10.1029/2006JC003750&lt;/a&gt;, 2007.</mixed-citation>
</ref>
<ref id="ref25">
<label>25</label><mixed-citation publication-type="other" xlink:type="simple">Schmid, M., Busbridge, M., and Wüest, A.: Double diffusive convection in Lake Kivu, Limnol. Oceanogr., 55, 225–238, &lt;a href=&quot;http://dx.doi.org/10.4319/lo.2010.55.1.0225&quot;&gt;https://doi.org/10.4319/lo.2010.55.1.0225&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref26">
<label>26</label><mixed-citation publication-type="other" xlink:type="simple">Schmitt, R. W.: Double diffusion in oceanography, Annu. Rev. Fluid Mech., 26, 255–285, &lt;a href=&quot;http://dx.doi.org/10.1146/annurev.fl.26.010194.001351&quot;&gt;https://doi.org/10.1146/annurev.fl.26.010194.001351&lt;/a&gt;, 1994.</mixed-citation>
</ref>
<ref id="ref27">
<label>27</label><mixed-citation publication-type="other" xlink:type="simple">Siggia, E. B.: High Rayleigh number convection, Annu. Rev. Fluid Mech., 26, 137–168, &lt;a href=&quot;http://dx.doi.org/10.1146/annurev.fl.26.010194.001033&quot;&gt;https://doi.org/10.1146/annurev.fl.26.010194.001033&lt;/a&gt;, 1994.</mixed-citation>
</ref>
<ref id="ref28">
<label>28</label><mixed-citation publication-type="other" xlink:type="simple">Swift, S. A., Bower, A. S., and Schmitt, R. W.: Vertical, horizontal, and temporal changes in temperature in the Atlantis II and Discovery hot brine pools, Red Sea, Deep Sea Res.-Pt. I, 64, 118–128, &lt;a href=&quot;http://dx.doi.org/10.1016/j.dsr.2012.02.006&quot;&gt;https://doi.org/10.1016/j.dsr.2012.02.006&lt;/a&gt;, 2012.</mixed-citation>
</ref>
<ref id="ref29">
<label>29</label><mixed-citation publication-type="other" xlink:type="simple">Timmermans, M. L. and Garrett, C.: Evolution of the deep water in the Canadian Basin of the Arctic Ocean, J. Phys. Oceanogr., 36, 866–874, &lt;a href=&quot;http://dx.doi.org/10.1175/JPO2906.1&quot;&gt;https://doi.org/10.1175/JPO2906.1&lt;/a&gt;, 2006.</mixed-citation>
</ref>
<ref id="ref30">
<label>30</label><mixed-citation publication-type="other" xlink:type="simple">Timmermans, M. L., Garrett, C., and Carmack, E.: The thermohaline structure and evolution of the deep waters in the Canada Basin, Arctic Ocean, Deep Sea Res.-Pt. I, 50, 1305–1321, &lt;a href=&quot;http://dx.doi.org/10.1016/S0967-0637(03)00125-0&quot;&gt;https://doi.org/10.1016/S0967-0637(03)00125-0&lt;/a&gt;, 2003.</mixed-citation>
</ref>
<ref id="ref31">
<label>31</label><mixed-citation publication-type="other" xlink:type="simple">Timmermans, M. L., Rainville, L., Thomas, L., and Proshutinsky, A.: Moored observations of bottom-intensified motions in the deep Canada Basin, Arctic Ocean, J. Mar. Res., 68, 625–641, &lt;a href=&quot;http://dx.doi.org/10.1357/002224010794657137&quot;&gt;https://doi.org/10.1357/002224010794657137&lt;/a&gt;, 2010.</mixed-citation>
</ref>
<ref id="ref32">
<label>32</label><mixed-citation publication-type="other" xlink:type="simple">Turner, J. S.: The coupled turbulent transport of salt and heat across a sharp density interface, Int. J. Heat Mass Tran., 8, 759–767, &lt;a href=&quot;http://dx.doi.org/10.1016/0017-9310(65)90022-0&quot;&gt;https://doi.org/10.1016/0017-9310(65)90022-0&lt;/a&gt;, 1965.</mixed-citation>
</ref>
<ref id="ref33">
<label>33</label><mixed-citation publication-type="other" xlink:type="simple">Turner, J. S.: The behavior of a stable salinity gradient heated from below, J. Fluid Mech., 33, 183–200, &lt;a href=&quot;http://dx.doi.org/10.1017/S0022112068002442&quot;&gt;https://doi.org/10.1017/S0022112068002442&lt;/a&gt;, 1968.</mixed-citation>
</ref>
<ref id="ref34">
<label>34</label><mixed-citation publication-type="other" xlink:type="simple">Turner, J. S.: Buoyancy Effects in Fluids, Cambridge University Press, 1973.</mixed-citation>
</ref>
<ref id="ref35">
<label>35</label><mixed-citation publication-type="other" xlink:type="simple">Veronis, G.: On finite amplitude instability in thermohaline convection, J . Mar. Res., 23, 1–17, 1965.</mixed-citation>
</ref>
<ref id="ref36">
<label>36</label><mixed-citation publication-type="other" xlink:type="simple">Voorhis, A. D. and Dorson, D. L.: Thermal convection in the Atlantis II hot brine pool, Deep Sea Res., 22, 167–175, &lt;a href=&quot;http://dx.doi.org/10.1016/0011-7471(75)90056-X&quot;&gt;https://doi.org/10.1016/0011-7471(75)90056-X&lt;/a&gt;, 1975.</mixed-citation>
</ref>
<ref id="ref37">
<label>37</label><mixed-citation publication-type="other" xlink:type="simple">Worster, M. G.: Time-dependent fluxes across double-diffusive interfaces, J. Fluid Mech., 505, 287–307, &lt;a href=&quot;http://dx.doi.org/10.1017/S0022112004008523&quot;&gt;https://doi.org/10.1017/S0022112004008523&lt;/a&gt;, 2004.</mixed-citation>
</ref>
<ref id="ref38">
<label>38</label><mixed-citation publication-type="other" xlink:type="simple">Zaussinger, F. and Spruit, H. C.: Semiconvection: numerical simulations, Astron. Astrophys., 554, A119, &lt;a href=&quot;http://dx.doi.org/10.1051/0004-6361/201220573&quot;&gt;https://doi.org/10.1051/0004-6361/201220573&lt;/a&gt;, 2013.</mixed-citation>
</ref>
<ref id="ref39">
<label>39</label><mixed-citation publication-type="other" xlink:type="simple">Zhou, S.-Q. and Lu, Y.-Z.: Characterizations of Double Diffusive Convection Steps and Heat Budget in the Deep Arctic Ocean, J. Geophys. Res., 118, 1–15, &lt;a href=&quot;http://dx.doi.org/10.1002/2013JC009141&quot;&gt;https://doi.org/10.1002/2013JC009141&lt;/a&gt;, 2013.</mixed-citation>
</ref>
</ref-list>
</back>
</article>