{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/127490"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/127490","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Unstable stokes waves in constant vorticity flows","abstract":"Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2026-12-01","abstract_html":"Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2026-12-01","abstract_has_math":false,"creators":["Hsiao, Ting-Yang"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Hur, Vera Mikyoung","Bronski, Jared","Tzirakis, Nikolaos","Zharnitsky, Vadim"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-12-06","date_published":"2024-12-06","updated_at":"2026-07-22T22:25:04Z","subjects":["Water Waves","Rotational Stokes Waves","Modulational Instability"],"languages":["en","eng"],"rights":["Copyright 2024 Ting-Yang Hsiao"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/127490","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hur, Vera Mikyoung","Bronski, Jared","Tzirakis, Nikolaos","Zharnitsky, Vadim"]},{"key":"dc:creator","label":"Author","values":["Hsiao, Ting-Yang"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2024-12-06","2024-12"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Water Waves","Rotational Stokes Waves","Modulational Instability"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2024 Ting-Yang Hsiao"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/127490"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2026-12-01","The student, Ting-Yang Hsiao, accepted the attached license on 2024-12-03 at 17:11.","The student, Ting-Yang Hsiao, submitted this Dissertation for approval on 2024-12-03 at 17:20.","This Dissertation was approved for publication on 2024-12-06 at 09:29.","DSpace SAF Submission Ingestion Package generated from Vireo submission #21481 on 2025-03-28 at 14:55:37","We delve into the modulational instability of small-amplitude, non-zero vorticity Stokes waves of the classical water-wave problem, which concerns the two-dimensional incompressible flow of a perfect fluid of unit depth under the force of gravity. The stability analysis method is based on a periodic Evans function approach developed recently by Hur and Yang for irrotational Stokes waves [1, 2] and center manifold mechanism to reduce the infinite-dimensional hydrodynamic problem to a four-dimensional space. We construct a modulational instability index, denoted indlow(ω, κ), depending on the vorticity ω and the wave number κ, and prove instability when indlow(ω, κ) > 0. Our result reproduces the Benjamin–Feir instability for κ > 1.3627827 . . . when vorticity is zero. For the non-zero vorticity case, we depict the stability/instability region. This modulational instability result rigorously justifies the NLS approximation of Thomas, Kharif, and Manna [3]"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Unstable stokes waves in constant vorticity flows"]}]}],"canonical_facts":{"dc:contributor":["Hur, Vera Mikyoung","Bronski, Jared","Tzirakis, Nikolaos","Zharnitsky, Vadim"],"dc:creator":["Hsiao, Ting-Yang"],"dc:date":["2024-12-06","2024-12"],"dc:description":["Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2026-12-01","The student, Ting-Yang Hsiao, accepted the attached license on 2024-12-03 at 17:11.","The student, Ting-Yang Hsiao, submitted this Dissertation for approval on 2024-12-03 at 17:20.","This Dissertation was approved for publication on 2024-12-06 at 09:29.","DSpace SAF Submission Ingestion Package generated from Vireo submission #21481 on 2025-03-28 at 14:55:37","We delve into the modulational instability of small-amplitude, non-zero vorticity Stokes waves of the classical water-wave problem, which concerns the two-dimensional incompressible flow of a perfect fluid of unit depth under the force of gravity. The stability analysis method is based on a periodic Evans function approach developed recently by Hur and Yang for irrotational Stokes waves [1, 2] and center manifold mechanism to reduce the infinite-dimensional hydrodynamic problem to a four-dimensional space. We construct a modulational instability index, denoted indlow(ω, κ), depending on the vorticity ω and the wave number κ, and prove instability when indlow(ω, κ) > 0. Our result reproduces the Benjamin–Feir instability for κ > 1.3627827 . . . when vorticity is zero. For the non-zero vorticity case, we depict the stability/instability region. This modulational instability result rigorously justifies the NLS approximation of Thomas, Kharif, and Manna [3]"],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/127490"],"dc:language":["en","eng"],"dc:rights":["Copyright 2024 Ting-Yang Hsiao"],"dc:subject":["Water Waves","Rotational Stokes Waves","Modulational Instability"],"dc:title":["Unstable stokes waves in constant vorticity flows"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:04Z"}