{"id":"https://openalex.org/W7212060728","doi":"https://doi.org/10.48550/arxiv.2609.05839","title":"Unsteady Thin-Airfoil Theory Revisited: An Approximate Analytical Solution and the Self-Similar Wagner Effect in Viscous Flows","display_name":"Unsteady Thin-Airfoil Theory Revisited: An Approximate Analytical Solution and the Self-Similar Wagner Effect in Viscous Flows","publication_year":2026,"publication_date":"2026-09-05","ids":{"openalex":"https://openalex.org/W7212060728","doi":"https://doi.org/10.48550/arxiv.2609.05839"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.05839","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.05839","pdf_url":"https://arxiv.org/pdf/2609.05839","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.05839","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151015821","display_name":"Tianshu Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I141649380","display_name":"Western Michigan University","ror":"https://ror.org/04j198w64","country_code":"US","type":"education","lineage":["https://openalex.org/I141649380"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Liu, Tianshu","raw_affiliation_strings":[": Department of Mechanical and Aerospace Engineering Western Michigan University , Kalamazoo , MI 49008 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":": Department of Mechanical and Aerospace Engineering Western Michigan University , Kalamazoo , MI 49008 , USA","institution_ids":["https://openalex.org/I141649380"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5150891021","display_name":"Jianfeng Lin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210157653","display_name":"Institute of Mechanics","ror":"https://ror.org/057jnjd73","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210157653"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lin, Jianfeng","raw_affiliation_strings":[": LNM , Institute of Mechanics Chinese Academy of Sciences , Beijing , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":": LNM , Institute of Mechanics Chinese Academy of Sciences , Beijing , China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210157653"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5150933364","display_name":"Shizhao Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210157653","display_name":"Institute of Mechanics","ror":"https://ror.org/057jnjd73","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210157653"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wang, Shizhao","raw_affiliation_strings":[": LNM , Institute of Mechanics Chinese Academy of Sciences , Beijing , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":": LNM , Institute of Mechanics Chinese Academy of Sciences , Beijing , China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210157653"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13951","display_name":"Fluid dynamics and aerodynamics studies","score":0.7768999934196472,"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/T13951","display_name":"Fluid dynamics and aerodynamics studies","score":0.7768999934196472,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.09359999746084213,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.037700001150369644,"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/wagner-effect","display_name":"Wagner effect","score":0.824999988079071},{"id":"https://openalex.org/keywords/wagner-function","display_name":"Wagner function","score":0.8029999732971191},{"id":"https://openalex.org/keywords/theodorsen-function","display_name":"Theodorsen function","score":0.9419999718666077},{"id":"https://openalex.org/keywords/unsteady-lift","display_name":"unsteady lift","score":0.8370000123977661},{"id":"https://openalex.org/keywords/self-similarity","display_name":"self-similarity","score":0.8349999785423279},{"id":"https://openalex.org/keywords/starting-flow","display_name":"starting flow","score":0.6850000023841858},{"id":"https://openalex.org/keywords/low-reynolds-number-flow","display_name":"low Reynolds number flow","score":0.6549999713897705},{"id":"https://openalex.org/keywords/flow-separation","display_name":"flow separation","score":0.703000009059906},{"id":"https://openalex.org/keywords/flat-plate-airfoil","display_name":"flat plate airfoil","score":0.9470000267028809},{"id":"https://openalex.org/keywords/viscous-flow","display_name":"viscous flow","score":0.546999990940094}],"concepts":[{"id":"https://openalex.org/C112124176","wikidata":"https://www.wikidata.org/wiki/Q4698744","display_name":"Airfoil","level":2,"score":0.8434000015258789},{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.6347000002861023},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5752999782562256},{"id":"https://openalex.org/C48939323","wikidata":"https://www.wikidata.org/wiki/Q294879","display_name":"Wake","level":2,"score":0.5449000000953674},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4997999966144562},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4878000020980835},{"id":"https://openalex.org/C150486481","wikidata":"https://www.wikidata.org/wiki/Q760106","display_name":"Lift coefficient","level":4,"score":0.4708000123500824},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4625999927520752},{"id":"https://openalex.org/C182748727","wikidata":"https://www.wikidata.org/wiki/Q178932","display_name":"Reynolds number","level":3,"score":0.45399999618530273},{"id":"https://openalex.org/C3019068222","wikidata":"https://www.wikidata.org/wiki/Q216320","display_name":"Unsteady flow","level":2,"score":0.41940000653266907},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.40149998664855957},{"id":"https://openalex.org/C131043120","wikidata":"https://www.wikidata.org/wiki/Q1543991","display_name":"Potential flow","level":2,"score":0.4000999927520752},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3815999925136566},{"id":"https://openalex.org/C200114574","wikidata":"https://www.wikidata.org/wiki/Q1143513","display_name":"Vorticity","level":3,"score":0.3720000088214874},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3587000072002411},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.34599998593330383},{"id":"https://openalex.org/C2777152854","wikidata":"https://www.wikidata.org/wiki/Q7306329","display_name":"Reduced frequency","level":4,"score":0.33149999380111694},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.33090001344680786},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.3057999908924103},{"id":"https://openalex.org/C2777447984","wikidata":"https://www.wikidata.org/wiki/Q23304018","display_name":"Two-dimensional flow","level":3,"score":0.3052999973297119},{"id":"https://openalex.org/C77576233","wikidata":"https://www.wikidata.org/wiki/Q1545856","display_name":"Flow separation","level":3,"score":0.2782000005245209},{"id":"https://openalex.org/C1633027","wikidata":"https://www.wikidata.org/wiki/Q815820","display_name":"Computational fluid dynamics","level":2,"score":0.2761000096797943},{"id":"https://openalex.org/C178760647","wikidata":"https://www.wikidata.org/wiki/Q28129961","display_name":"Vortex shedding","level":4,"score":0.26570001244544983},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.26460000872612},{"id":"https://openalex.org/C18932819","wikidata":"https://www.wikidata.org/wiki/Q2029236","display_name":"Stream function","level":4,"score":0.26429998874664307},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.05839","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.05839","pdf_url":"https://arxiv.org/pdf/2609.05839","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.05839","doi":"https://doi.org/10.48550/arxiv.2609.05839","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.05839","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.05839","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.05839","pdf_url":"https://arxiv.org/pdf/2609.05839","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309563","display_name":"Western Michigan University","ror":"https://ror.org/04j198w64"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212060728.pdf","grobid_xml":"https://content.openalex.org/works/W7212060728.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4317632406","https://openalex.org/W2103166599","https://openalex.org/W2061715798","https://openalex.org/W2082126929","https://openalex.org/W353592611","https://openalex.org/W4402686490","https://openalex.org/W4280488959","https://openalex.org/W1609052929","https://openalex.org/W2080864662","https://openalex.org/W2021011753"],"abstract_inverted_index":{"An":[0],"approximate":[1,37],"analytical":[2,47,74],"solution":[3,38,48,75],"for":[4],"the":[5,24,40,52,58,63,69,79,87,92,95,104,115,125,138,146],"unsteady":[6,15],"lift":[7,98],"of":[8,39,62,94,124],"a":[9,13,20,83,109,128],"thin":[10],"airfoil":[11,131],"with":[12,82],"general":[14],"motion":[16],"is":[17,28,49,76,119,140],"derived":[18],"from":[19],"viscous-flow":[21],"perspective,":[22],"where":[23],"wake":[25],"vortex-sheet":[26],"strength":[27],"given":[29],"in":[30,86,108,121],"an":[31,36],"explicit":[32,59],"convolution-type":[33],"expression":[34],"as":[35,68],"Wagner":[41,53,64,89,106,117],"integral":[42,60],"equation.":[43],"For":[44],"validation,":[45],"this":[46,73],"applied":[50,77],"to":[51,78,103],"and":[54,65,100],"Theodorsen":[55,66],"problems,":[56],"giving":[57],"forms":[61],"functions":[67],"reduced":[70],"cases.":[71],"Further,":[72],"starting":[80,129],"flow":[81,126,139],"finite":[84,110],"timescale":[85],"generalized":[88],"problem,":[90],"revealing":[91],"self-similarity":[93,144],"re-normalized":[96,105],"circulatory":[97],"coefficient":[99],"its":[101],"equivalence":[102],"function":[107],"time":[111],"domain.":[112],"More":[113],"importantly,":[114],"self-similar":[116],"effect":[118],"found":[120],"numerical":[122],"simulation":[123],"over":[127],"flat-plate":[130],"at":[132],"low":[133],"Reynolds":[134],"numbers":[135],"even":[136],"when":[137],"moderately":[141],"separated.":[142],"This":[143],"represents":[145],"Reynolds-number-invariance.":[147]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-10T00:00:00"}