{"id":"https://openalex.org/W7204824930","doi":"https://doi.org/10.31223/x53f7g","title":"The four-vector potential of equatorial shallow water waves from Hamilton\u2019s principle","display_name":"The four-vector potential of equatorial shallow water waves from Hamilton\u2019s principle","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204824930","doi":"https://doi.org/10.31223/x53f7g"},"language":"en","primary_location":{"id":"doi:10.31223/x53f7g","doi":"https://doi.org/10.31223/x53f7g","is_oa":true,"landing_page_url":"https://doi.org/10.31223/x53f7g","pdf_url":"https://eartharxiv.org/repository/object/14708/download/25574/","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://eartharxiv.org/repository/object/14708/download/25574/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035126758","display_name":"Pao K. Wang","orcid":"https://orcid.org/0000-0003-2134-290X","observed_orcids":["https://orcid.org/0000-0003-2134-290X"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Pao Wang","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-2134-290X","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5035126758"],"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/T10255","display_name":"Oceanographic and Atmospheric Processes","score":0.8461999893188477,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10255","display_name":"Oceanographic and Atmospheric Processes","score":0.8461999893188477,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.0803999975323677,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.020400000736117363,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/shallow-water-waves","display_name":"shallow water waves","score":0.8399999737739563},{"id":"https://openalex.org/keywords/equatorial-beta-plane","display_name":"equatorial beta-plane","score":0.8230000138282776},{"id":"https://openalex.org/keywords/hamilton-s-principle","display_name":"Hamilton's principle","score":0.9259999990463257},{"id":"https://openalex.org/keywords/minimal-coupling","display_name":"minimal coupling","score":0.6769999861717224},{"id":"https://openalex.org/keywords/coriolis-force","display_name":"Coriolis force","score":0.8870000243186951},{"id":"https://openalex.org/keywords/rotating-flow","display_name":"rotating flow","score":0.6290000081062317},{"id":"https://openalex.org/keywords/variational-principle","display_name":"variational principle","score":0.7009999752044678},{"id":"https://openalex.org/keywords/quadratic-lagrangian","display_name":"quadratic Lagrangian","score":0.7200000286102295},{"id":"https://openalex.org/keywords/zonal-wavenumber","display_name":"zonal wavenumber","score":0.597000002861023}],"concepts":[{"id":"https://openalex.org/C186348155","wikidata":"https://www.wikidata.org/wiki/Q7975538","display_name":"Waves and shallow water","level":2,"score":0.6733999848365784},{"id":"https://openalex.org/C73421765","wikidata":"https://www.wikidata.org/wiki/Q1738426","display_name":"Kelvin wave","level":2,"score":0.6133999824523926},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6029000282287598},{"id":"https://openalex.org/C121130766","wikidata":"https://www.wikidata.org/wiki/Q192510","display_name":"Wavenumber","level":2,"score":0.5552999973297119},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.5457000136375427},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.4968000054359436},{"id":"https://openalex.org/C43058520","wikidata":"https://www.wikidata.org/wiki/Q624580","display_name":"Eulerian path","level":3,"score":0.4797999858856201},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.47620001435279846},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4580000042915344},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.447299987077713},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.43560001254081726},{"id":"https://openalex.org/C157216528","wikidata":"https://www.wikidata.org/wiki/Q1331126","display_name":"Velocity potential","level":3,"score":0.43529999256134033},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.4343999922275543},{"id":"https://openalex.org/C15227799","wikidata":"https://www.wikidata.org/wiki/Q6731684","display_name":"Magnetosphere particle motion","level":3,"score":0.42660000920295715},{"id":"https://openalex.org/C131043120","wikidata":"https://www.wikidata.org/wiki/Q1543991","display_name":"Potential flow","level":2,"score":0.38839998841285706},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.3736000061035156},{"id":"https://openalex.org/C86038547","wikidata":"https://www.wikidata.org/wiki/Q779457","display_name":"Particle displacement","level":3,"score":0.3734999895095825},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.3718999922275543},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3653999865055084},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.35519999265670776},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.35280001163482666},{"id":"https://openalex.org/C35048267","wikidata":"https://www.wikidata.org/wiki/Q587553","display_name":"Charged particle","level":3,"score":0.351500004529953},{"id":"https://openalex.org/C171889981","wikidata":"https://www.wikidata.org/wiki/Q1454008","display_name":"Free surface","level":2,"score":0.3483000099658966},{"id":"https://openalex.org/C160121416","wikidata":"https://www.wikidata.org/wiki/Q1423347","display_name":"Geopotential","level":2,"score":0.3465000092983246},{"id":"https://openalex.org/C32758168","wikidata":"https://www.wikidata.org/wiki/Q900488","display_name":"Normal mode","level":3,"score":0.31859999895095825},{"id":"https://openalex.org/C177562468","wikidata":"https://www.wikidata.org/wiki/Q182893","display_name":"Dispersion (optics)","level":2,"score":0.3165000081062317},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.3098999857902527},{"id":"https://openalex.org/C84174578","wikidata":"https://www.wikidata.org/wiki/Q889796","display_name":"Surface wave","level":2,"score":0.303600013256073},{"id":"https://openalex.org/C2778517922","wikidata":"https://www.wikidata.org/wiki/Q7140482","display_name":"Particle (ecology)","level":2,"score":0.29989999532699585},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29899999499320984},{"id":"https://openalex.org/C140295346","wikidata":"https://www.wikidata.org/wiki/Q4008384","display_name":"Shallow water equations","level":2,"score":0.2888999879360199},{"id":"https://openalex.org/C37222873","wikidata":"https://www.wikidata.org/wiki/Q17027571","display_name":"Horizontal plane","level":2,"score":0.2881999909877777},{"id":"https://openalex.org/C40308292","wikidata":"https://www.wikidata.org/wiki/Q122518","display_name":"Plane wave","level":2,"score":0.27469998598098755},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.27129998803138733},{"id":"https://openalex.org/C169596890","wikidata":"https://www.wikidata.org/wiki/Q661247","display_name":"Breaking wave","level":3,"score":0.2694999873638153},{"id":"https://openalex.org/C109626945","wikidata":"https://www.wikidata.org/wiki/Q961596","display_name":"Stokes drift","level":3,"score":0.2685999870300293},{"id":"https://openalex.org/C18932819","wikidata":"https://www.wikidata.org/wiki/Q2029236","display_name":"Stream function","level":4,"score":0.26570001244544983},{"id":"https://openalex.org/C2780759522","wikidata":"https://www.wikidata.org/wiki/Q7922828","display_name":"Vertical displacement","level":2,"score":0.2574000060558319},{"id":"https://openalex.org/C166693061","wikidata":"https://www.wikidata.org/wiki/Q5462119","display_name":"Flow velocity","level":3,"score":0.25519999861717224}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.31223/x53f7g","doi":"https://doi.org/10.31223/x53f7g","is_oa":true,"landing_page_url":"https://doi.org/10.31223/x53f7g","pdf_url":"https://eartharxiv.org/repository/object/14708/download/25574/","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},{"id":"pmh:oai:EA:id:14708","doi":null,"is_oa":true,"landing_page_url":"https://eartharxiv.org/repository/object/14708/download/25613/","pdf_url":"https://eartharxiv.org/repository/object/14708/download/25613/","source":{"id":"https://openalex.org/S4306402614","display_name":"EarthArXiv (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"EarthArXiv","raw_type":"PREPRINTS"}],"best_oa_location":{"id":"doi:10.31223/x53f7g","doi":"https://doi.org/10.31223/x53f7g","is_oa":true,"landing_page_url":"https://doi.org/10.31223/x53f7g","pdf_url":"https://eartharxiv.org/repository/object/14708/download/25574/","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320331164","display_name":"National Science and Technology Council","ror":"https://ror.org/00wnb9798"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204824930.pdf","grobid_xml":"https://content.openalex.org/works/W7204824930.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7204748181","https://openalex.org/W2067919295","https://openalex.org/W2441335658","https://openalex.org/W3003942491","https://openalex.org/W2024240547","https://openalex.org/W4239801430","https://openalex.org/W1988181463","https://openalex.org/W64790026","https://openalex.org/W2082258079","https://openalex.org/W575723214"],"abstract_inverted_index":{"Linear":[0],"shallow":[1,85],"water":[2,86],"waves":[3],"on":[4],"an":[5,143],"equatorial":[6],"\u03b2-plane":[7],"can":[8],"be":[9,51],"represented":[10],"as":[11],"the":[12,35,54,61,69,73,80,101,107,115,130,138,146],"states":[13],"of":[14,75,90,103,145],"a":[15,21,66,76,91,96,125],"charged":[16,93],"particle":[17,94],"minimally":[18],"coupled":[19],"to":[20,32,135],"four-vector":[22,116],"potential":[23,36,117],"whose":[24],"analogue":[25],"magnetic":[26],"field":[27,98],"is":[28,37,64,88,133,142],"uniform":[29,97],"and":[30,40,79,137],"proportional":[31],"\u03b2/c_g.":[33],"There":[34],"written":[38],"down":[39],"verified":[41],"rather":[42],"than":[43],"derived.":[44],"We":[45],"show":[46],"that":[47,89],"it":[48],"need":[49],"not":[50],"assumed.":[52],"In":[53],"Eulerian":[55],"variational":[56],"principle":[57],"for":[58,83],"rotating":[59],"flow":[60],"Coriolis":[62],"coupling":[63],"already":[65],"minimal":[67],"coupling,":[68],"frame":[70],"velocity":[71],"playing":[72],"part":[74],"vector":[77],"potential,":[78],"quadratic":[81],"Lagrangian":[82],"linear":[84],"motion":[87],"two-dimensional":[92],"in":[95,100,124],"acting":[99],"plane":[102],"parcel":[104],"displacement.":[105],"Eliminating":[106],"zonal":[108],"displacement":[109],"amplitude,":[110],"which":[111],"enters":[112],"algebraically,":[113],"returns":[114],"identically.":[118],"The":[119],"\u03b2k/\u03c9":[120],"term":[121],"then":[122],"originates":[123],"single":[126],"integration":[127],"by":[128],"parts,":[129],"vertical":[131],"wavenumber":[132],"forced":[134],"vanish,":[136],"potential\u2019s":[139],"frequency":[140],"dependence":[141],"artifact":[144],"reduction.":[147]},"counts_by_year":[],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-09-01T00:00:00"}