{"id":"https://openalex.org/W2035310570","doi":"https://doi.org/10.1142/s0218127402004401","title":"THE 1:2 MODE INTERACTION IN RAYLEIGH\u2013B\u00c9NARD CONVECTION WITH AND WITHOUT BOUSSINESQ SYMMETRY","display_name":"THE 1:2 MODE INTERACTION IN RAYLEIGH\u2013B\u00c9NARD CONVECTION WITH AND WITHOUT BOUSSINESQ SYMMETRY","publication_year":2002,"publication_date":"2002-02-01","ids":{"openalex":"https://openalex.org/W2035310570","doi":"https://doi.org/10.1142/s0218127402004401","mag":"2035310570"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127402004401","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127402004401","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066794191","display_name":"Joana d\u2019Arc Prat Farran","orcid":"https://orcid.org/0000-0001-7628-487X"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"JOANA PRAT","raw_affiliation_strings":["Departament de Matem\u00e0tica Aplicada IV, Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tica Aplicada IV, Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060506408","display_name":"Isabel Mercader","orcid":"https://orcid.org/0000-0002-0749-0263"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"ISABEL MERCADER","raw_affiliation_strings":["Departament de F\u00edsica Aplicada,  Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departament de F\u00edsica Aplicada,  Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065649147","display_name":"Edgar Knobloch","orcid":"https://orcid.org/0000-0002-1567-9314"},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"EDGAR KNOBLOCH","raw_affiliation_strings":["Department of Applied Mathematics, University of Leeds,  Leeds LS2 9JT, UK","Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Leeds,  Leeds LS2 9JT, UK","institution_ids":["https://openalex.org/I130828816"]},{"raw_affiliation_string":"Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, UK,","institution_ids":["https://openalex.org/I130828816"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5066794191"],"corresponding_institution_ids":["https://openalex.org/I9617848"],"apc_list":null,"apc_paid":null,"fwci":1.3939,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.80270482,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"12","issue":"02","first_page":"281","last_page":"308"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12141","display_name":"Fluid Dynamics and Thin Films","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/prandtl-number","display_name":"Prandtl number","score":0.8637003898620605},{"id":"https://openalex.org/keywords/convection","display_name":"Convection","score":0.6877690553665161},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.6515324115753174},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5739713311195374},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.5304210782051086},{"id":"https://openalex.org/keywords/rayleigh-number","display_name":"Rayleigh number","score":0.5196398496627808},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.51882404088974},{"id":"https://openalex.org/keywords/reflection-symmetry","display_name":"Reflection symmetry","score":0.5037829279899597},{"id":"https://openalex.org/keywords/rayleigh\u2013b\u00e9nard-convection","display_name":"Rayleigh\u2013B\u00e9nard convection","score":0.4319297671318054},{"id":"https://openalex.org/keywords/rayleigh-scattering","display_name":"Rayleigh scattering","score":0.43156009912490845},{"id":"https://openalex.org/keywords/boundary-layer","display_name":"Boundary layer","score":0.42993465065956116},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.4246859848499298},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3683655261993408},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3122260570526123},{"id":"https://openalex.org/keywords/natural-convection","display_name":"Natural convection","score":0.2576372027397156},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.24871107935905457},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.15929311513900757},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10141494870185852}],"concepts":[{"id":"https://openalex.org/C72687893","wikidata":"https://www.wikidata.org/wiki/Q815306","display_name":"Prandtl number","level":3,"score":0.8637003898620605},{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.6877690553665161},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6515324115753174},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5739713311195374},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5304210782051086},{"id":"https://openalex.org/C106836276","wikidata":"https://www.wikidata.org/wiki/Q898249","display_name":"Rayleigh number","level":4,"score":0.5196398496627808},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.51882404088974},{"id":"https://openalex.org/C133978748","wikidata":"https://www.wikidata.org/wiki/Q15955882","display_name":"Reflection symmetry","level":2,"score":0.5037829279899597},{"id":"https://openalex.org/C132812236","wikidata":"https://www.wikidata.org/wiki/Q1019460","display_name":"Rayleigh\u2013B\u00e9nard convection","level":5,"score":0.4319297671318054},{"id":"https://openalex.org/C46244369","wikidata":"https://www.wikidata.org/wiki/Q193709","display_name":"Rayleigh scattering","level":2,"score":0.43156009912490845},{"id":"https://openalex.org/C111603439","wikidata":"https://www.wikidata.org/wiki/Q752193","display_name":"Boundary layer","level":2,"score":0.42993465065956116},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.4246859848499298},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3683655261993408},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3122260570526123},{"id":"https://openalex.org/C54791560","wikidata":"https://www.wikidata.org/wiki/Q3285020","display_name":"Natural convection","level":3,"score":0.2576372027397156},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.24871107935905457},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.15929311513900757},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10141494870185852}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127402004401","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127402004401","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W380173811","https://openalex.org/W1965778005","https://openalex.org/W1972700216","https://openalex.org/W1974619653","https://openalex.org/W1976884116","https://openalex.org/W1999183691","https://openalex.org/W2010641231","https://openalex.org/W2017896395","https://openalex.org/W2024389736","https://openalex.org/W2047254719","https://openalex.org/W2053376060","https://openalex.org/W2055098614","https://openalex.org/W2066087421","https://openalex.org/W2068117918","https://openalex.org/W2073847384","https://openalex.org/W2079262489","https://openalex.org/W2087268763","https://openalex.org/W2088770048","https://openalex.org/W2089876099","https://openalex.org/W2094254700","https://openalex.org/W2100386495","https://openalex.org/W2100942321","https://openalex.org/W2118662912","https://openalex.org/W2122099244","https://openalex.org/W2167262170","https://openalex.org/W2168865944","https://openalex.org/W2324409378","https://openalex.org/W3040940214","https://openalex.org/W4231871155","https://openalex.org/W4234820192","https://openalex.org/W4253294199"],"related_works":["https://openalex.org/W2295618585","https://openalex.org/W3022851647","https://openalex.org/W1973994006","https://openalex.org/W2018472114","https://openalex.org/W2049083135","https://openalex.org/W4323569755","https://openalex.org/W2005060967","https://openalex.org/W2002402484","https://openalex.org/W1989791522","https://openalex.org/W2997852510"],"abstract_inverted_index":{"Nonlinear":[0],"two-dimensional":[1],"Rayleigh\u2013B\u00e9nard":[2],"convection":[3,32],"with":[4],"periodic":[5],"boundary":[6,24,51],"conditions":[7,25,52],"in":[8],"the":[9,17,27,42,50,54,69,76,89],"horizontal":[10],"is":[11,33,46,79,85,91,99],"studied":[12],"for":[13,101],"spatial":[14],"periods":[15],"near":[16],"1:2":[18,77],"steady":[19],"state":[20],"mode":[21],"interaction.":[22],"The":[23,93],"at":[26,53],"bottom":[28],"are":[29,67],"no-slip,":[30],"and":[31,64,75,88,106,113],"driven":[34],"by":[35],"a":[36],"fixed":[37],"imposed":[38],"temperature":[39],"difference":[40],"across":[41],"layer.":[43],"Homotopic":[44],"continuation":[45],"used":[47],"to":[48,59],"continue":[49],"top":[55],"from":[56],"no-slip":[57],"(\u03b2=0)":[58],"stress-free":[60],"(\u03b2=1).":[61],"When":[62,81],"\u03b2=0":[63],"non-Boussinesq":[65],"effects":[66],"absent":[68],"system":[70],"has":[71],"midplane":[72],"reflection":[73],"symmetry":[74,84],"resonance":[78,90],"weak.":[80],"\u03b2=1":[82],"this":[83],"strongly":[86],"broken":[87],"strong.":[92],"transition":[94],"between":[95],"these":[96],"two":[97,102],"cases":[98],"explored":[100],"Prandtl":[103,115],"numbers,":[104,116],"\u03c3=10":[105],"\u03c3=0.1,":[107],"representing":[108],"behavior":[109],"typical":[110],"of":[111],"large":[112],"low":[114],"respectively.":[117]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}