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<div class=Section1>
<p class=MsoNormal style='background:white'><cite><span style='font-family:
"Arial","sans-serif";color:#666666'>Science </span></cite><span
class=apple-converted-space><span style='font-family:"Arial","sans-serif";
color:#666666'> </span></span><span style='font-family:"Arial","sans-serif";
color:#666666'>24 Nov 2017:<br>
Vol. 358, Issue 6366, pp. 990-991<br>
DOI: 10.1126/science.aaq0469<o:p></o:p></span></p>
<h1 style='mso-margin-top-alt:0in;margin-right:0in;margin-bottom:11.25pt;
margin-left:0in;background:white'><span style='font-size:18.0pt;font-family:
"Arial","sans-serif";color:#333333'><o:p> </o:p></span></h1>
<h1 style='mso-margin-top-alt:0in;margin-right:0in;margin-bottom:11.25pt;
margin-left:0in;background:white'><span style='font-size:18.0pt;font-family:
"Arial","sans-serif";color:#333333'>Why do Earth's equatorial waves head east?<o:p></o:p></span></h1>
<p class=MsoNormal style='margin-left:0in;text-indent:-.25in;line-height:18.0pt;
mso-list:l8 level1 lfo1;background:white'><![if !supportLists]><span lang=ES
style='font-family:"Arial","sans-serif"'><span style='mso-list:Ignore'>1.<span
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
class=name><span lang=ES style='font-family:"Arial","sans-serif"'>Joseph A.
Biello</span></span><span lang=ES style='font-family:"Arial","sans-serif"'>,<span
class=apple-converted-space> </span><span class=name>Tudor Dimofte</span><o:p></o:p></span></p>
<h2 style='mso-margin-top-alt:22.5pt;margin-right:0in;margin-bottom:0in;
margin-left:0in;margin-bottom:.0001pt;background:white'><span style='font-family:
"Arial","sans-serif";color:#333333'>Summary<o:p></o:p></span></h2>
<p style='mso-margin-top-alt:2.8pt;margin-right:0in;margin-bottom:0in;
margin-left:0in;margin-bottom:.0001pt;line-height:18.0pt;background:white;
box-sizing: inherit;transition: background-color 1s ease-in-out 1s' id=p-3><span
style='font-family:"Arial","sans-serif";color:#333333'>Equatorial Kelvin waves
occur constantly in Earth's atmosphere and ocean. They constitute an isolated
and powerful component of the observed atmospheric wave spectrum (<em><span
style='font-family:"Arial","sans-serif"'>1</span></em>), whereas oceanic Kelvin
waves drive up- and downwelling in the Pacific Ocean thermocline, which affects
the El Niño–Southern Oscillation. In the atmosphere, Kelvin waves are
initiated by and coupled to convective activity (storm systems), mostly over
the Indian and the western Pacific Oceans, whereas in periods of large-scale
convective organization, such as the Madden-Julian Oscillation, equatorial
Kelvin wave activity is suppressed. On page</span><span
class=apple-converted-space><span style='font-family:"Arial","sans-serif";
color:#333333'> </span></span><span style='font-family:"Arial","sans-serif";
color:#333333'><a
href="http://science.sciencemag.org/lookup/doi/10.1126/science.aan8819"><b><span
style='color:#37588A'>1075</span></b></a></span><span
class=apple-converted-space><span style='font-family:"Arial","sans-serif";
color:#333333'> </span></span><span style='font-family:"Arial","sans-serif";
color:#333333'>of this issue, Delplace</span><span class=apple-converted-space><span
style='font-family:"Arial","sans-serif";color:#333333'> </span></span><em><span
style='font-family:"Arial","sans-serif";color:#333333'>et al.</span></em><span
class=apple-converted-space><span style='font-family:"Arial","sans-serif";
color:#333333'> </span></span><span style='font-family:"Arial","sans-serif";
color:#333333'>(<em><span style='font-family:"Arial","sans-serif"'>2</span></em>)
attempt to answer the questions of why there are three equatorially confined
waves, and why they all have eastward group velocity. They propose a
fascinating perspective on the existence of unidirectional, equatorially
confined atmospheric waves by developing an analogy with similar phenomena that
occur in electronic materials—in particular, in quantum Hall states and
topological insulators.<o:p></o:p></span></p>
<p style='mso-margin-top-alt:2.8pt;margin-right:0in;margin-bottom:0in;
margin-left:0in;margin-bottom:.0001pt;line-height:18.0pt;background:white'><span
style='font-family:"Arial","sans-serif";color:#333333'><o:p> </o:p></span></p>
<p style='mso-margin-top-alt:2.8pt;margin-right:0in;margin-bottom:0in;
margin-left:0in;margin-bottom:.0001pt;line-height:18.0pt;background:white'><span
style='font-family:"Arial","sans-serif";color:#333333'>/////////////////////////////<o:p></o:p></span></p>
<p style='mso-margin-top-alt:2.8pt;margin-right:0in;margin-bottom:0in;
margin-left:0in;margin-bottom:.0001pt;line-height:18.0pt;background:white'><span
style='font-family:"Arial","sans-serif";color:#333333'><o:p> </o:p></span></p>
<p class=MsoNormal style='background:white'><cite><span style='font-family:
"Arial","sans-serif";color:#666666'>Science </span></cite><span
class=apple-converted-space><span style='font-family:"Arial","sans-serif";
color:#666666'> </span></span><span style='font-family:"Arial","sans-serif";
color:#666666'>24 Nov 2017:<br>
Vol. 358, Issue 6366, pp. 1075-1077<br>
DOI: 10.1126/science.aan8819<o:p></o:p></span></p>
<p style='mso-margin-top-alt:2.8pt;margin-right:0in;margin-bottom:0in;
margin-left:0in;margin-bottom:.0001pt;line-height:18.0pt;background:white'><span
style='font-family:"Arial","sans-serif";color:#333333'><o:p> </o:p></span></p>
<h1 style='mso-margin-top-alt:0in;margin-right:0in;margin-bottom:11.25pt;
margin-left:0in;background:white'><span style='font-size:18.0pt;font-family:
"Arial","sans-serif";color:#333333'>Topological origin of equatorial waves<o:p></o:p></span></h1>
<p class=MsoNormal style='margin-left:0in;text-indent:-.25in;line-height:18.0pt;
mso-list:l4 level1 lfo6;background:white'><![if !supportLists]><span lang=FR
style='font-family:"Helvetica","sans-serif"'><span style='mso-list:Ignore'>1.<span
style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span
class=name><span lang=FR style='font-family:"Helvetica","sans-serif"'>Pierre
Delplace</span></span><span style='font-family:"Helvetica","sans-serif"'><a
href="http://science.sciencemag.org/content/358/6366/1075?utm_campaign=toc_sci-mag_2017-11-22&et_rid=34815706&et_cid=1680339#aff-1"
id=xref-aff-1-1><sup><span lang=FR style='font-size:8.0pt;color:windowtext;
border:none windowtext 1.0pt;padding:0in'>1</span></sup></a></span><span
class=xref-sep><span lang=FR style='font-size:8.0pt;font-family:"Helvetica","sans-serif"'>,</span></span><span
style='font-family:"Helvetica","sans-serif"'><a
href="http://science.sciencemag.org/content/358/6366/1075?utm_campaign=toc_sci-mag_2017-11-22&et_rid=34815706&et_cid=1680339#corresp-1"
id=xref-corresp-1-1><span lang=FR style='font-size:8.0pt;color:windowtext;
border:none windowtext 1.0pt;padding:0in'>*</span></a></span><span lang=FR
style='font-family:"Helvetica","sans-serif"'>,<span
class=apple-converted-space> </span><span class=name>J. B. Marston</span></span><span
style='font-family:"Helvetica","sans-serif"'><a
href="http://science.sciencemag.org/content/358/6366/1075?utm_campaign=toc_sci-mag_2017-11-22&et_rid=34815706&et_cid=1680339#aff-2"
id=xref-aff-2-1><sup><span lang=FR style='font-size:8.0pt;color:windowtext;
border:none windowtext 1.0pt;padding:0in'>2</span></sup></a></span><span
class=xref-sep><span lang=FR style='font-size:8.0pt;font-family:"Helvetica","sans-serif"'>,</span></span><span
style='font-family:"Helvetica","sans-serif"'><a
href="http://science.sciencemag.org/content/358/6366/1075?utm_campaign=toc_sci-mag_2017-11-22&et_rid=34815706&et_cid=1680339#corresp-1"
id=xref-corresp-1-2><span lang=FR style='font-size:8.0pt;color:windowtext;
border:none windowtext 1.0pt;padding:0in'>*</span></a></span><span lang=FR
style='font-family:"Helvetica","sans-serif"'>,<span
class=apple-converted-space> </span><span class=name>Antoine Venaille</span></span><span
style='font-family:"Helvetica","sans-serif"'><a
href="http://science.sciencemag.org/content/358/6366/1075?utm_campaign=toc_sci-mag_2017-11-22&et_rid=34815706&et_cid=1680339#aff-1"
id=xref-aff-1-2><sup><span lang=FR style='font-size:8.0pt;color:windowtext;
border:none windowtext 1.0pt;padding:0in'>1</span></sup></a></span><span
class=xref-sep><span lang=FR style='font-size:8.0pt;font-family:"Helvetica","sans-serif"'>,</span></span><span
style='font-family:"Helvetica","sans-serif"'><a
href="http://science.sciencemag.org/content/358/6366/1075?utm_campaign=toc_sci-mag_2017-11-22&et_rid=34815706&et_cid=1680339#corresp-1"
id=xref-corresp-1-3><span lang=FR style='font-size:8.0pt;color:windowtext;
border:none windowtext 1.0pt;padding:0in'>*</span></a></span><span lang=FR
style='font-family:"Helvetica","sans-serif"'><o:p></o:p></span></p>
<p class=MsoNormal style='mso-margin-top-alt:auto;margin-left:0in;text-indent:
-.25in;line-height:18.0pt;mso-list:l0 level1 lfo10;background:white;box-sizing: inherit;
cursor:pointer;font-size:0.75rem'><![if !supportLists]><span lang=FR
style='font-size:10.0pt;font-family:Symbol;color:#333333'><span
style='mso-list:Ignore'>·<span style='font:7.0pt "Times New Roman"'>
</span></span></span><![endif]><span lang=FR style='font-family:"Roboto","serif";
color:#333333'><o:p> </o:p></span></p>
<h2 style='margin:0in;margin-bottom:.0001pt;background:#E6E6E6;box-sizing: inherit;
font-size:1.5rem'><span style='font-family:"Arial","sans-serif";color:#333333'>Fluid
waves with topological origins<o:p></o:p></span></h2>
<p style='mso-margin-top-alt:2.8pt;margin-right:0in;margin-bottom:11.25pt;
margin-left:0in;line-height:18.0pt;background:#E6E6E6;box-sizing: inherit;
transition: background-color 1s ease-in-out 1s' id=p-2><span style='font-family:
"Arial","sans-serif";color:#333333'>Topological effects that arise from
material boundaries are well known in solid-state physics and form the basis
for topological insulators. Delplace<span class=apple-converted-space> </span><em><span
style='font-family:"Arial","sans-serif"'>et al.</span></em><span
class=apple-converted-space> </span>describe atmospheric and ocean waves
that appear to have a similar topological origin (see the Perspective by Biello
and Dimofte). The waves exist because of the symmetry-breaking nature of
Earth's rotation, which allows certain fixed topological constraints on the
system. These findings may be useful for understanding a wide variety of
geophysical and astrophysical flows.<o:p></o:p></span></p>
<p style='mso-margin-top-alt:11.25pt;margin-right:0in;margin-bottom:0in;
margin-left:0in;margin-bottom:.0001pt;line-height:18.0pt;background:#E6E6E6;
box-sizing: inherit;transition: background-color 1s ease-in-out 1s' id=p-3><em><span
style='font-family:"Arial","sans-serif";color:#333333'>Science</span></em><span
style='font-family:"Arial","sans-serif";color:#333333'>, this issue p.<span
class=apple-converted-space> </span><a
href="http://science.sciencemag.org/lookup/doi/10.1126/science.aan8819"><b><span
style='color:#37588A'>1075</span></b></a>; see also p.<span
class=apple-converted-space> </span><a
href="http://science.sciencemag.org/lookup/doi/10.1126/science.aaq0469"><b><span
style='color:#37588A'>990</span></b></a><o:p></o:p></span></p>
<p style='mso-margin-top-alt:11.25pt;margin-right:0in;margin-bottom:0in;
margin-left:0in;margin-bottom:.0001pt;line-height:18.0pt;background:#E6E6E6'><span
style='font-family:"Arial","sans-serif";color:#333333'><o:p> </o:p></span></p>
<h2 style='margin:0in;margin-bottom:.0001pt;background:#E6E6E6;box-sizing: inherit;
font-size:1.5rem'><span style='font-family:"Arial","sans-serif";color:#333333'>Abstract<o:p></o:p></span></h2>
<p style='mso-margin-top-alt:2.8pt;margin-right:0in;margin-bottom:0in;
margin-left:0in;margin-bottom:.0001pt;line-height:18.0pt;background:#E6E6E6;
box-sizing: inherit;transition: background-color 1s ease-in-out 1s' id=p-5><span
style='font-family:"Arial","sans-serif";color:#333333'>Topology sheds new light
on the emergence of unidirectional edge waves in a variety of physical systems,
from condensed matter to artificial lattices. Waves observed in geophysical
flows are also robust to perturbations, which suggests a role for topology. We
show a topological origin for two well-known equatorially trapped waves, the
Kelvin and Yanai modes, owing to the breaking of time-reversal symmetry by
Earth’s rotation. The nontrivial structure of the bulk Poincaré wave
modes encoded through the first Chern number of value 2 guarantees the
existence of these waves. This invariant demonstrates that ocean and
atmospheric waves share fundamental properties with topological insulators and
that topology plays an unexpected role in Earth’s climate system.<o:p></o:p></span></p>
<p style='mso-margin-top-alt:2.8pt;margin-right:0in;margin-bottom:0in;
margin-left:0in;margin-bottom:.0001pt;line-height:18.0pt;background:white'><span
style='font-family:"Arial","sans-serif";color:#333333'><o:p> </o:p></span></p>
<p class=MsoNormal><o:p> </o:p></p>
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