{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/23125"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/23125","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Derivation of an Evolution Equation for Two-Dimensional Waves on Thin Films","abstract":"We examine wave propagation on thin liquid films subjected to gravity, fluid friction, surface tension, and Marangoni effects. The physical configuration is a thin liquid layer on a planar incline. Following previous studies, the Marangoni effect is incorporated by a constant surface tension gradient and yields a non-convex flux function in our thin film equation. We extend previous studies by deriving the thin film equation governing two-dimensional waves on the liquid layer. We then derive a simplified evolution equation governing weakly nonlinear, quasi-planar, and weakly dissipative waves on the layer. When the undisturbed state is in the vicinity of an inflection point in the streamwise component of the flux function, the mixed nonlinearity, fourth order dissipation and the transverse modulations interact over time scales on the order of the scaled amplitude to the negative second power. The effect the transverse modulations is found to be intrinsically nonlinear.","abstract_html":"We examine wave propagation on thin liquid films subjected to gravity, fluid friction, surface tension, and Marangoni effects. The physical configuration is a thin liquid layer on a planar incline. Following previous studies, the Marangoni effect is incorporated by a constant surface tension gradient and yields a non-convex flux function in our thin film equation. We extend previous studies by deriving the thin film equation governing two-dimensional waves on the liquid layer. We then derive a simplified evolution equation governing weakly nonlinear, quasi-planar, and weakly dissipative waves on the layer. When the undisturbed state is in the vicinity of an inflection point in the streamwise component of the flux function, the mixed nonlinearity, fourth order dissipation and the transverse modulations interact over time scales on the order of the scaled amplitude to the negative second power. The effect the transverse modulations is found to be intrinsically nonlinear.","abstract_has_math":false,"creators":["Goodnight, Randall James Truett"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Engineering Mechanics","degree_department":"Engineering Science and Mechanics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Cramer, Mark S."],"committee_members":["Ragab, Saad A.","Jung, Sunghwan"],"year":2013,"date_issued":"2013-06-01","date_published":"2013-06-01","updated_at":"2026-07-22T22:18:47Z","subjects":["Thin Films","Undercompressive Shock","Non-Convex Flux","Marangoni Stress","Surface Tensio"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:1280"],"render_values":[{"text":"vt_gsexam:1280","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/23125","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Cramer, Mark S."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Ragab, Saad A.","Jung, Sunghwan"]},{"key":"dc:contributor.department","label":"Department","values":["Engineering Science and Mechanics"]},{"key":"dc:creator","label":"Author","values":["Goodnight, Randall James Truett"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2013-06-02T08:00:30Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2013-06-02T08:00:30Z"]},{"key":"dc:date.issued","label":"Date","values":["2013-06-01"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Engineering Mechanics"]},{"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":["Thin Films","Undercompressive Shock","Non-Convex Flux","Marangoni Stress","Surface Tensio"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"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":["vt_gsexam:1280"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/23125"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We examine wave propagation on thin liquid films subjected to gravity, fluid friction, surface tension, and Marangoni effects. The physical configuration is a thin liquid layer on a planar incline. Following previous studies, the Marangoni effect is incorporated by a constant surface tension gradient and yields a non-convex flux function in our thin film equation. We extend previous studies by deriving the thin film equation governing two-dimensional waves on the liquid layer. We then derive a simplified evolution equation governing weakly nonlinear, quasi-planar, and weakly dissipative waves on the layer. When the undisturbed state is in the vicinity of an inflection point in the streamwise component of the flux function, the mixed nonlinearity, fourth order dissipation and the transverse modulations interact over time scales on the order of the scaled amplitude to the negative second power. The effect the transverse modulations is found to be intrinsically nonlinear."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["Derivation of an Evolution Equation for Two-Dimensional Waves on Thin Films"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Cramer, Mark S."],"dc:contributor.committeemember":["Ragab, Saad A.","Jung, Sunghwan"],"dc:contributor.department":["Engineering Science and Mechanics"],"dc:creator":["Goodnight, Randall James Truett"],"dc:date.accessioned":["2013-06-02T08:00:30Z"],"dc:date.available":["2013-06-02T08:00:30Z"],"dc:date.issued":["2013-06-01"],"dc:description.abstract":["We examine wave propagation on thin liquid films subjected to gravity, fluid friction, surface tension, and Marangoni effects. The physical configuration is a thin liquid layer on a planar incline. Following previous studies, the Marangoni effect is incorporated by a constant surface tension gradient and yields a non-convex flux function in our thin film equation. We extend previous studies by deriving the thin film equation governing two-dimensional waves on the liquid layer. We then derive a simplified evolution equation governing weakly nonlinear, quasi-planar, and weakly dissipative waves on the layer. When the undisturbed state is in the vicinity of an inflection point in the streamwise component of the flux function, the mixed nonlinearity, fourth order dissipation and the transverse modulations interact over time scales on the order of the scaled amplitude to the negative second power. The effect the transverse modulations is found to be intrinsically nonlinear."],"dc:description.degree":["Master of Science"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:1280"],"dc:identifier.uri":["http://hdl.handle.net/10919/23125"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Thin Films","Undercompressive Shock","Non-Convex Flux","Marangoni Stress","Surface Tensio"],"dc:title":["Derivation of an Evolution Equation for Two-Dimensional Waves on Thin Films"],"dc:type":["Thesis"],"thesis:degree_discipline":["Engineering Mechanics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:18:47Z"}