{"doi":"10.1063/1.868750","title":"A theory of three-dimensional interfacial vorticity dynamics","abstract":"<jats:p>A three-dimensional theory of vorticity dynamics on an incompressible viscous and immiscible fluid–fluid interface, or interfacial vorticity dynamics for short, is presented as a counterpart of the vorticity dynamics on an arbitrarily curved rigid wall [J. Fluid Mech. 254, 183 (1993)]. General formulas with arbitrary Reynolds numbers Re are derived for determining (1) how much vorticity exists on an interface S, (2) how much vorticity is created from S and sent into the fluid per unit area in per unit time, and (3) the force and moment acted on a closed interface by the created vorticity thereon. The common feature and fundamental difference between interfacial vorticity dynamics and its rigid-wall counterpart are analyzed. In particular, on a free surface, the primary driving mechanism of vorticity creation is the balance between the shear stress (measured by tangent vorticity) and the tangent components of the surface-deformation stress alone, which results in a weak creation rate of O (Re−1/2) at large Re. Therefore, the exact form of the theory with its full complexity is of importance mainly at low Reynolds numbers, especially in understanding the small-scale coherent structures of interfacial turbulence. The vorticity creation rate at high-Re approximations, including an interfacial boundary layer of finite thickness and the limit of Re→∞ (the so-called Euler limit), is also studied, both allowing for a rotational inviscid outer flow. While for the former this leads to a generalization of Lundgren’s theory [in Mathematic Aspects of Vortex Dynamics, edited by R. E. Caflish (SIAM, Philadelphia, PA, 1989), pp. 68–79] and amounts to solving a linear boundary-layer problem, for the latter the creation rate can be directly obtained from an inviscid solution, leading to a dynamic evolution equation of interfacial vortex sheet. In three dimensions, a vortex sheet may bifurcate into a normal vorticity field, upon which the dependence of the sheet velocity is determined. A few examples are examined to illustrate different aspects and approximation levels of the general theory.</jats:p>","journal":"Physics of Fluids","year":1995,"id":29409,"datarank":4.42955789090003,"base_score":4.127134385045092,"endowment":4.127134385045092,"self_citation_contribution":0.6190701577567639,"citation_network_contribution":3.810487733143266,"self_endowment_contribution":0.6190701577567639,"citer_contribution":3.810487733143266,"corpus_percentile":null,"corpus_rank":null,"citation_count":61,"citer_count":60,"citers_with_citation_signal":53,"citers_with_endowment":53,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_data_producer":false,"deposit_databanks":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":162263,"name":"Jie-Zhi Wu","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"base_score":4.127134385045092,"endowment":4.127134385045092,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"18998881","pmcid":null,"openalex_id":"https://openalex.org/W2049790739","authors":[],"funders":[],"total_grants":0,"fwci":2.7229,"citation_percentile":0.89083762,"influential_citations":10,"citation_trend":[{"year":2012,"count":1},{"year":2014,"count":2},{"year":2016,"count":2},{"year":2018,"count":1},{"year":2020,"count":1},{"year":2021,"count":7},{"year":2022,"count":6},{"year":2023,"count":6},{"year":2024,"count":5},{"year":2025,"count":2},{"year":2026,"count":3}],"oa_status":"closed","license":null,"oa_locations":[{"url":"https://pubs.aip.org/aip/pof/article-pdf/7/10/2375/19296767/2375_1_online.pdf","host_type":"publisher"},{"url":"https://doi.org/10.1063/1.868750","host_type":"journal"}],"fields_of_study":["Fluid Dynamics and Turbulent Flows","Particle Dynamics in Fluid Flows","Fluid Dynamics and Vibration Analysis","Physics"],"mesh_terms":[],"keywords":["Vorticity","Burgers vortex","Physics","Vorticity equation","Vortex stretching","Inviscid flow","Classical mechanics","Vortex","Mechanics","Euler equations","Boundary layer","Reynolds stress","Turbulence","Thermodynamics"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-06-08T23:42:23.375207Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}