<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-05384231</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-19T07:25:00+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">From a vortex gas to a vortex crystal in instability-driven two-dimensional turbulence</title>
            <author role="aut">
              <persName>
                <forename type="first">Adrian</forename>
                <surname>van Kan</surname>
              </persName>
              <email type="md5">280c8b906491bb7a1b66e403451da20d</email>
              <email type="domain">berkeley.edu</email>
              <idno type="idhal" notation="numeric">1187225</idno>
              <idno type="halauthorid" notation="string">1721049-1187225</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-1217-3609</idno>
              <affiliation ref="#struct-563719"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Benjamin</forename>
                <surname>Favier</surname>
              </persName>
              <email type="md5">757cb8413ccb6dc6856734279a9a1c7e</email>
              <email type="domain">irphe.univ-mrs.fr</email>
              <idno type="idhal" notation="string">benjamin-favier</idno>
              <idno type="idhal" notation="numeric">3684</idno>
              <idno type="halauthorid" notation="string">9847-3684</idno>
              <idno type="RESEARCHERID">http://www.researcherid.com/rid/C-1969-2012</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-1184-2989</idno>
              <idno type="IDREF">https://www.idref.fr/140863885</idno>
              <idno type="RESEARCHERID">http://www.researcherid.com/rid/http://www.researcherid.com/rid/C-1969-2012</idno>
              <affiliation ref="#struct-196526"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Keith</forename>
                <surname>Julien</surname>
              </persName>
              <idno type="idhal" notation="numeric">1358607</idno>
              <idno type="halauthorid" notation="string">2389471-1358607</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-4409-7022</idno>
              <affiliation ref="#struct-302215"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Edgar</forename>
                <surname>Knobloch</surname>
              </persName>
              <idno type="idhal" notation="numeric">1609118</idno>
              <idno type="halauthorid" notation="string">731412-1609118</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-1567-9314</idno>
              <affiliation ref="#struct-563719"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Benjamin</forename>
                <surname>Favier</surname>
              </persName>
              <email type="md5">757cb8413ccb6dc6856734279a9a1c7e</email>
              <email type="domain">irphe.univ-mrs.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2025-11-26 18:40:54</date>
              <date type="whenModified">2025-11-27 03:20:26</date>
              <date type="whenReleased">2025-11-26 18:50:45</date>
              <date type="whenProduced">2024</date>
              <date type="whenEndEmbargoed">2025-11-26</date>
              <ref type="file" target="https://hal.science/hal-05384231v1/document">
                <date notBefore="2025-11-26"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-05384231v1/file/2308.08789v2.pdf" id="file-5384231-4607890">
                <date notBefore="2025-11-26"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/2308.08789"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="313427">
                <persName>
                  <forename>Benjamin</forename>
                  <surname>Favier</surname>
                </persName>
                <email type="md5">757cb8413ccb6dc6856734279a9a1c7e</email>
                <email type="domain">irphe.univ-mrs.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-05384231</idno>
            <idno type="halUri">https://hal.science/hal-05384231</idno>
            <idno type="halBibtex">vankan:hal-05384231</idno>
            <idno type="halRefHtml">&lt;i&gt;Journal of Fluid Mechanics&lt;/i&gt;, 2024, 984, pp.A41. &lt;a target="_blank" href="https://dx.doi.org/10.1017/jfm.2024.162"&gt;&amp;#x27E8;10.1017/jfm.2024.162&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Journal of Fluid Mechanics, 2024, 984, pp.A41. &amp;#x27E8;10.1017/jfm.2024.162&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-5384231-4607890"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-AMU">Aix Marseille Université</idno>
            <idno type="stamp" n="IRPHE">Institut de Recherche sur les Phenomenes Hors Equilibre</idno>
            <idno type="stamp" n="EC-MARSEILLE">Ecole Centrale de Marseille</idno>
            <idno type="stamp" n="PEIRESC">Fédération Fabri de Peiresc</idno>
            <idno type="stamp" n="IMI-AMU">Institut Mécanique et Ingénierie</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">From a vortex gas to a vortex crystal in instability-driven two-dimensional turbulence</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Adrian</forename>
                    <surname>van Kan</surname>
                  </persName>
                  <email type="md5">280c8b906491bb7a1b66e403451da20d</email>
                  <email type="domain">berkeley.edu</email>
                  <idno type="idhal" notation="numeric">1187225</idno>
                  <idno type="halauthorid" notation="string">1721049-1187225</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-1217-3609</idno>
                  <affiliation ref="#struct-563719"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Benjamin</forename>
                    <surname>Favier</surname>
                  </persName>
                  <email type="md5">757cb8413ccb6dc6856734279a9a1c7e</email>
                  <email type="domain">irphe.univ-mrs.fr</email>
                  <idno type="idhal" notation="string">benjamin-favier</idno>
                  <idno type="idhal" notation="numeric">3684</idno>
                  <idno type="halauthorid" notation="string">9847-3684</idno>
                  <idno type="RESEARCHERID">http://www.researcherid.com/rid/C-1969-2012</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-1184-2989</idno>
                  <idno type="IDREF">https://www.idref.fr/140863885</idno>
                  <idno type="RESEARCHERID">http://www.researcherid.com/rid/http://www.researcherid.com/rid/C-1969-2012</idno>
                  <affiliation ref="#struct-196526"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Keith</forename>
                    <surname>Julien</surname>
                  </persName>
                  <idno type="idhal" notation="numeric">1358607</idno>
                  <idno type="halauthorid" notation="string">2389471-1358607</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-4409-7022</idno>
                  <affiliation ref="#struct-302215"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Edgar</forename>
                    <surname>Knobloch</surname>
                  </persName>
                  <idno type="idhal" notation="numeric">1609118</idno>
                  <idno type="halauthorid" notation="string">731412-1609118</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-1567-9314</idno>
                  <affiliation ref="#struct-563719"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">6127</idno>
                <idno type="issn">0022-1120</idno>
                <idno type="eissn">1469-7645</idno>
                <title level="j">Journal of Fluid Mechanics</title>
                <imprint>
                  <publisher>Cambridge University Press (CUP)</publisher>
                  <biblScope unit="volume">984</biblScope>
                  <biblScope unit="pp">A41</biblScope>
                  <date type="datePub">2024</date>
                </imprint>
              </monogr>
              <idno type="arxiv">2308.08789</idno>
              <idno type="doi">10.1017/jfm.2024.162</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="phys.meca.mefl">Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph]</classCode>
              <classCode scheme="halDomain" n="nlin.nlin-ps">Nonlinear Sciences [physics]/Pattern Formation and Solitons [nlin.PS]</classCode>
              <classCode scheme="halDomain" n="phys.cond.cm-scm">Physics [physics]/Condensed Matter [cond-mat]/Soft Condensed Matter [cond-mat.soft]</classCode>
              <classCode scheme="halDomain" n="phys.phys.phys-ao-ph">Physics [physics]/Physics [physics]/Atmospheric and Oceanic Physics [physics.ao-ph]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We study structure formation in two-dimensional turbulence driven by an external force, interpolating between linear instability forcing and random stirring, subject to nonlinear damping. Using extensive direct numerical simulations, we uncover a rich parameter space featuring four distinct branches of stationary solutions: large-scale vortices, hybrid states with embedded shielded vortices (SVs) of either sign, and two states composed of many similar SVs. Of the latter, the first is a dense vortex gas where all SVs have the same sign and diffuse across the domain. The second is a hexagonal vortex crystal forming from this gas when the linear instability is sufficiently weak. These solutions coexist stably over a wide parameter range. The late-time evolution of the system from small-amplitude initial conditions is nearly self-similar, involving three phases: initial inverse cascade, random nucleation of SVs from turbulence and, once a critical number of vortices is reached, a phase of explosive nucleation of SVs, leading to a statistically stationary state. The vortex gas is continued in the forcing parameter, revealing a sharp transition towards the crystal state as the forcing strength decreases. This transition is analysed based on the diffusion of individual vortices and using statistical physics. The crystal can also decay via an inverse cascade resulting from the breakdown of shielding or insufficient nonlinear damping acting on SVs. Our study highlights the importance of the forcing details in two-dimensional turbulence and reveals the presence of nontrivial SV states in this system, specifically the emergence and melting of a vortex crystal.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="institution" xml:id="struct-563719" status="VALID">
          <idno type="ROR">https://ror.org/01an7q238</idno>
          <orgName>University of California [Berkeley]</orgName>
          <orgName type="acronym">UC Berkeley</orgName>
          <desc>
            <address>
              <addrLine>Berkeley, CA</addrLine>
              <country key="US"/>
            </address>
            <ref type="url">https://www.berkeley.edu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-471291" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-196526" status="VALID">
          <idno type="IdRef">077932757</idno>
          <idno type="RNSR">201220273N</idno>
          <idno type="ROR">03zq0xc17</idno>
          <orgName>Institut de Recherche sur les Phénomènes Hors Equilibre</orgName>
          <orgName type="acronym">IRPHE</orgName>
          <date type="start">1995-01-01</date>
          <desc>
            <address>
              <addrLine>Technopole de Chateau-Gombert - 49 rue Joliot Curie - BP 146 - 13384 MARSEILLE cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.irphe.univ-mrs.fr</ref>
          </desc>
          <listRelation>
            <relation name="UMR7342 / UMR6594 / UMR138" active="#struct-198056" type="direct"/>
            <relation active="#struct-300415" type="direct"/>
            <relation name="UMR7342 / UMR6594 / UMR138" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-302215" status="VALID">
          <idno type="ROR">https://ror.org/02ttsq026</idno>
          <orgName>University of Colorado [Boulder]</orgName>
          <desc>
            <address>
              <addrLine>Boulder, Colorado 80309</addrLine>
              <country key="US"/>
            </address>
            <ref type="url">http://www.colorado.edu/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-471291" status="VALID">
          <idno type="ROR">https://ror.org/00pjdza24</idno>
          <orgName>University of California</orgName>
          <orgName type="acronym">UC</orgName>
          <date type="start">1869-01-01</date>
          <desc>
            <address>
              <country key="US"/>
            </address>
            <ref type="url">https://www.universityofcalifornia.edu/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-198056" status="VALID">
          <idno type="IdRef">15863621X</idno>
          <idno type="ISNI">0000 0001 2176 4817</idno>
          <idno type="ROR">https://ror.org/035xkbk20</idno>
          <orgName>Aix Marseille Université</orgName>
          <orgName type="acronym">AMU</orgName>
          <date type="start">2012-01-01</date>
          <desc>
            <address>
              <addrLine>Aix-Marseille UniversitéJardins du Pharo58 Boulevard Charles Livon13284 Marseille cedex 7</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-amu.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300415" status="VALID">
          <idno type="ISNI">0000 0004 1762 2703</idno>
          <idno type="ROR">https://ror.org/040baw385</idno>
          <orgName>École Centrale de Marseille</orgName>
          <orgName type="acronym">ECM</orgName>
          <date type="start">2006-09-27</date>
          <desc>
            <address>
              <addrLine>Pôle de l'étoile - Technopole de Château-Gombert - 38 rue Frédéric Joliot-Curie - 13013 Marseille</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.centrale-marseille.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>