{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/69777"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/69777","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Vortex Flows: The Dynamics of Shear Layers and Hill's Vortex","abstract":"We study the dynamics of flows with concentrated vorticity by analyzing the nonlinear instability of free vortex layers and Hill's vortex. The evolution is calculated numerically employing the contour dynamics formulation. We show that the growth of small, monochromatic perturbations on unstable vortex layers leads to the development of elliptical vortices whose asymptotic behavior is a function of the initial layer thickness and the form of the perturbation. Subharmonic disturbances initiate an interaction between vortices which may result in coalescence of large vortices and orbiting motion of small vortices. The calculations provide a criterion for the minimum vortex size required for coalescence. This phenomenon explains the transition to stochastic behavior characteristic of turbulent flows.","abstract_html":"We study the dynamics of flows with concentrated vorticity by analyzing the nonlinear instability of free vortex layers and Hill's vortex. The evolution is calculated numerically employing the contour dynamics formulation. We show that the growth of small, monochromatic perturbations on unstable vortex layers leads to the development of elliptical vortices whose asymptotic behavior is a function of the initial layer thickness and the form of the perturbation. Subharmonic disturbances initiate an interaction between vortices which may result in coalescence of large vortices and orbiting motion of small vortices. The calculations provide a criterion for the minimum vortex size required for coalescence. This phenomenon explains the transition to stochastic behavior characteristic of turbulent flows.","abstract_has_math":false,"creators":["Pozrikidis, Constantine"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Chemical Engineering","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-15T19:54:34Z","date_published":"2014-12-15T19:54:34Z","updated_at":"2026-07-22T22:26:01Z","subjects":["Engineering, Chemical"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8711855"],"render_values":[{"text":"(UMI)AAI8711855","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/69777","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Pozrikidis, Constantine"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-15T19:54:34Z","10000-01-01","1987"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Chemical Engineering"]},{"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":["Engineering, Chemical"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/69777","(UMI)AAI8711855"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We study the dynamics of flows with concentrated vorticity by analyzing the nonlinear instability of free vortex layers and Hill's vortex. The evolution is calculated numerically employing the contour dynamics formulation. We show that the growth of small, monochromatic perturbations on unstable vortex layers leads to the development of elliptical vortices whose asymptotic behavior is a function of the initial layer thickness and the form of the perturbation. Subharmonic disturbances initiate an interaction between vortices which may result in coalescence of large vortices and orbiting motion of small vortices. The calculations provide a criterion for the minimum vortex size required for coalescence. This phenomenon explains the transition to stochastic behavior characteristic of turbulent flows.","To investigate the dynamics of wake type flows, we consider the instability of two attached vortex layers with opposite vorticity. Depending on the layer thicknesses, the evolution may lead to diverse behavior including formation of a stable vortex street, dispersion of the circulation into small vortex blobs and development of vortex dipoles.","For axisymmetric flows, we analyze the instability of Hill's vortex subject to axisymmetric perturbations. We find that prolate perturbations cause the formation of a vortex tail behind the spherical core, while oblate perturbations lead to the development of a nearly steady vortex ring. The asymptotic state is a function of the amplitude of the initial perturbation. The asymptotic rings arising from oblate vortices are similar to steady rings described by previous authors (Norbury, 1973).","Made available in DSpace on 2014-12-15T19:54:34Z (GMT). No. of bitstreams: 1 8711855.pdf: 7821136 bytes, checksum: 1a4fd382a1e2bc3638910bbea79484d7 (MD5) Previous issue date: 1987","Embargo set by: Seth Robbins for item 69943 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","313 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1987."]},{"key":"dc:title","label":"Title","values":["Vortex Flows: The Dynamics of Shear Layers and Hill's Vortex"]}]}],"canonical_facts":{"dc:creator":["Pozrikidis, Constantine"],"dc:date":["2014-12-15T19:54:34Z","10000-01-01","1987"],"dc:description":["We study the dynamics of flows with concentrated vorticity by analyzing the nonlinear instability of free vortex layers and Hill's vortex. The evolution is calculated numerically employing the contour dynamics formulation. We show that the growth of small, monochromatic perturbations on unstable vortex layers leads to the development of elliptical vortices whose asymptotic behavior is a function of the initial layer thickness and the form of the perturbation. Subharmonic disturbances initiate an interaction between vortices which may result in coalescence of large vortices and orbiting motion of small vortices. The calculations provide a criterion for the minimum vortex size required for coalescence. This phenomenon explains the transition to stochastic behavior characteristic of turbulent flows.","To investigate the dynamics of wake type flows, we consider the instability of two attached vortex layers with opposite vorticity. Depending on the layer thicknesses, the evolution may lead to diverse behavior including formation of a stable vortex street, dispersion of the circulation into small vortex blobs and development of vortex dipoles.","For axisymmetric flows, we analyze the instability of Hill's vortex subject to axisymmetric perturbations. We find that prolate perturbations cause the formation of a vortex tail behind the spherical core, while oblate perturbations lead to the development of a nearly steady vortex ring. The asymptotic state is a function of the amplitude of the initial perturbation. The asymptotic rings arising from oblate vortices are similar to steady rings described by previous authors (Norbury, 1973).","Made available in DSpace on 2014-12-15T19:54:34Z (GMT). No. of bitstreams: 1 8711855.pdf: 7821136 bytes, checksum: 1a4fd382a1e2bc3638910bbea79484d7 (MD5) Previous issue date: 1987","Embargo set by: Seth Robbins for item 69943 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","313 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1987."],"dc:identifier":["http://hdl.handle.net/2142/69777","(UMI)AAI8711855"],"dc:subject":["Engineering, Chemical"],"dc:title":["Vortex Flows: The Dynamics of Shear Layers and Hill's Vortex"],"dc:type":["text"],"thesis:degree_discipline":["Chemical Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:01Z"}