{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/42902"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/42902","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Linear stability analysis of circular jets: integer, fractional, and multiple mode excitation","abstract":"The linear stability analysis of Huang [1995] has been adapted to ignore the effects of swirl, and to allow calculation of the eigenvalues and eigenfunctions for integer, fractional, and multiple modes of excitation. The investigation was intended to be exploratory; to gain the best possible insights into the flow characteristics from analysis of the linearized Euler equations. All of the azimuthal modes investigated (one-half, one, three-halves, and two) were found to lead to the continuous, helical, vortical structure evolution in the streamwise direction of the jet. The analysis for fractional modes of excitation predicted aphysical behavior near the jet center that has been attributed to a unresolved questions in the mathematical analysis of the problem. Multiple mode excitation at the axisymmetric mode and one or more azimuthal modes were found to result in un-even, periodic, vortex-ring growth in the shear layer. An argument was presented for the axisymmetric mode (m=O) resulting in the highest levels of entrainment for all integer, fractional, and multiple modes of excitation. Finally the importance of the azimuthal component of vorticity in the entrainment process was identified.","abstract_html":"The linear stability analysis of Huang [1995] has been adapted to ignore the effects of swirl, and to allow calculation of the eigenvalues and eigenfunctions for integer, fractional, and multiple modes of excitation. The investigation was intended to be exploratory; to gain the best possible insights into the flow characteristics from analysis of the linearized Euler equations. All of the azimuthal modes investigated (one-half, one, three-halves, and two) were found to lead to the continuous, helical, vortical structure evolution in the streamwise direction of the jet. The analysis for fractional modes of excitation predicted aphysical behavior near the jet center that has been attributed to a unresolved questions in the mathematical analysis of the problem. Multiple mode excitation at the axisymmetric mode and one or more azimuthal modes were found to result in un-even, periodic, vortex-ring growth in the shear layer. An argument was presented for the axisymmetric mode (m=O) resulting in the highest levels of entrainment for all integer, fractional, and multiple modes of excitation. Finally the importance of the azimuthal component of vorticity in the entrainment process was identified.","abstract_has_math":false,"creators":["Leimkuhler, Matthew Pancoast"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mechanical Engineering","degree_department":"Mechanical Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1995,"date_issued":"1995-12-05","date_published":"1995-12-05","updated_at":"2026-07-22T22:19:00Z","subjects":["flow characteristics"],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-06082009-170937"],"render_values":[{"text":"etd-06082009-170937","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/42902","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Mechanical Engineering"]},{"key":"dc:creator","label":"Author","values":["Leimkuhler, Matthew Pancoast"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:37:08Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:37:08Z","2009-06-08"]},{"key":"dc:date.issued","label":"Date","values":["1995-12-05"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["flow characteristics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-06082009-170937"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/42902"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The linear stability analysis of Huang [1995] has been adapted to ignore the effects of swirl, and to allow calculation of the eigenvalues and eigenfunctions for integer, fractional, and multiple modes of excitation. The investigation was intended to be exploratory; to gain the best possible insights into the flow characteristics from analysis of the linearized Euler equations. All of the azimuthal modes investigated (one-half, one, three-halves, and two) were found to lead to the continuous, helical, vortical structure evolution in the streamwise direction of the jet. The analysis for fractional modes of excitation predicted aphysical behavior near the jet center that has been attributed to a unresolved questions in the mathematical analysis of the problem. Multiple mode excitation at the axisymmetric mode and one or more azimuthal modes were found to result in un-even, periodic, vortex-ring growth in the shear layer. An argument was presented for the axisymmetric mode (m=O) resulting in the highest levels of entrainment for all integer, fractional, and multiple modes of excitation. Finally the importance of the azimuthal component of vorticity in the entrainment process was identified."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["BTD"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Linear stability analysis of circular jets: integer, fractional, and multiple mode excitation"]}]}],"canonical_facts":{"dc:contributor.department":["Mechanical Engineering"],"dc:creator":["Leimkuhler, Matthew Pancoast"],"dc:date.accessioned":["2014-03-14T21:37:08Z"],"dc:date.available":["2014-03-14T21:37:08Z","2009-06-08"],"dc:date.issued":["1995-12-05"],"dc:description.abstract":["The linear stability analysis of Huang [1995] has been adapted to ignore the effects of swirl, and to allow calculation of the eigenvalues and eigenfunctions for integer, fractional, and multiple modes of excitation. 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