{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/53832"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/53832","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Catenaries in Viscous Fluid","abstract":"Slender structures in fluid flow exhibit a variety of rich behaviors. Here we study the equilibrium shapes of perfectly flexible strings that are moving with a uniform velocity and axial flow in viscous fluid. The string is acted upon by local, anisotropic, linear drag forces and a uniform body force. Generically, the configurations of the string are planar, and we provide analytical expressions for the equilibrium shapes of the string as a first order five parameter dynamical system for the tangential angle of the body ($theta$). Phase portraits in the angle-curvature ($theta,partial_s theta$) plane are generated, that can be shown to be $pi$ periodic after appropriate scaling and reflection operations. The rich parameter space allows for different kinds of phase portraits that give rise to a variety of curve geometries. Some of these solutions are unstable due to the presence of compressive stresses. Special cases of the problem include sedimenting filaments, dynamic catenaries, and towed strings. We also discuss equilibrium configurations of towed cables and other relevant problems with fixed boundary conditions. Special cases of the boundary value problem involve towing of neutrally buoyant cables and strings with pure axial flow between two fixed points.","abstract_html":"Slender structures in fluid flow exhibit a variety of rich behaviors. Here we study the equilibrium shapes of perfectly flexible strings that are moving with a uniform velocity and axial flow in viscous fluid. The string is acted upon by local, anisotropic, linear drag forces and a uniform body force. Generically, the configurations of the string are planar, and we provide analytical expressions for the equilibrium shapes of the string as a first order five parameter dynamical system for the tangential angle of the body ($theta$). Phase portraits in the angle-curvature (<span class=\"etd-inline-math\">theta,partial<sub>s</sub> theta</span>) plane are generated, that can be shown to be $pi$ periodic after appropriate scaling and reflection operations. The rich parameter space allows for different kinds of phase portraits that give rise to a variety of curve geometries. Some of these solutions are unstable due to the presence of compressive stresses. Special cases of the problem include sedimenting filaments, dynamic catenaries, and towed strings. We also discuss equilibrium configurations of towed cables and other relevant problems with fixed boundary conditions. Special cases of the boundary value problem involve towing of neutrally buoyant cables and strings with pure axial flow between two fixed points.","abstract_has_math":true,"creators":["Chakrabarti, Brato"],"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":["Hanna, James"],"committee_members":["Ross, Shane D.","Stremler, Mark A."],"year":2015,"date_issued":"2015-06-26","date_published":"2015-06-26","updated_at":"2026-07-22T22:20:34Z","subjects":["Catenary","String","Towing","Dynamical System","Phase Portrait","Viscous Flow"],"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:5600"],"render_values":[{"text":"vt_gsexam:5600","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/53832","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Hanna, James"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Ross, Shane D.","Stremler, Mark A."]},{"key":"dc:contributor.department","label":"Department","values":["Engineering Science and Mechanics"]},{"key":"dc:creator","label":"Author","values":["Chakrabarti, Brato"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2015-06-27T08:00:21Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2015-06-27T08:00:21Z"]},{"key":"dc:date.issued","label":"Date","values":["2015-06-26"]},{"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":["Catenary","String","Towing","Dynamical System","Phase Portrait","Viscous Flow"]}]},{"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:5600"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/53832"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Slender structures in fluid flow exhibit a variety of rich behaviors. Here we study the equilibrium shapes of perfectly flexible strings that are moving with a uniform velocity and axial flow in viscous fluid. The string is acted upon by local, anisotropic, linear drag forces and a uniform body force. Generically, the configurations of the string are planar, and we provide analytical expressions for the equilibrium shapes of the string as a first order five parameter dynamical system for the tangential angle of the body ($theta$). Phase portraits in the angle-curvature ($theta,partial_s theta$) plane are generated, that can be shown to be $pi$ periodic after appropriate scaling and reflection operations. The rich parameter space allows for different kinds of phase portraits that give rise to a variety of curve geometries. Some of these solutions are unstable due to the presence of compressive stresses. Special cases of the problem include sedimenting filaments, dynamic catenaries, and towed strings. We also discuss equilibrium configurations of towed cables and other relevant problems with fixed boundary conditions. Special cases of the boundary value problem involve towing of neutrally buoyant cables and strings with pure axial flow between two fixed points."]},{"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":["Catenaries in Viscous Fluid"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Hanna, James"],"dc:contributor.committeemember":["Ross, Shane D.","Stremler, Mark A."],"dc:contributor.department":["Engineering Science and Mechanics"],"dc:creator":["Chakrabarti, Brato"],"dc:date.accessioned":["2015-06-27T08:00:21Z"],"dc:date.available":["2015-06-27T08:00:21Z"],"dc:date.issued":["2015-06-26"],"dc:description.abstract":["Slender structures in fluid flow exhibit a variety of rich behaviors. Here we study the equilibrium shapes of perfectly flexible strings that are moving with a uniform velocity and axial flow in viscous fluid. The string is acted upon by local, anisotropic, linear drag forces and a uniform body force. Generically, the configurations of the string are planar, and we provide analytical expressions for the equilibrium shapes of the string as a first order five parameter dynamical system for the tangential angle of the body ($theta$). Phase portraits in the angle-curvature ($theta,partial_s theta$) plane are generated, that can be shown to be $pi$ periodic after appropriate scaling and reflection operations. The rich parameter space allows for different kinds of phase portraits that give rise to a variety of curve geometries. Some of these solutions are unstable due to the presence of compressive stresses. Special cases of the problem include sedimenting filaments, dynamic catenaries, and towed strings. We also discuss equilibrium configurations of towed cables and other relevant problems with fixed boundary conditions. Special cases of the boundary value problem involve towing of neutrally buoyant cables and strings with pure axial flow between two fixed points."],"dc:description.degree":["Master of Science"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:5600"],"dc:identifier.uri":["http://hdl.handle.net/10919/53832"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Catenary","String","Towing","Dynamical System","Phase Portrait","Viscous Flow"],"dc:title":["Catenaries in Viscous Fluid"],"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":"2026-07-22T22:20:34Z"}