Catenaries in Viscous Fluid

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dc.contributor.authorChakrabarti, Bratoen
dc.contributor.committeechairHanna, Jamesen
dc.contributor.committeememberRoss, Shane D.en
dc.contributor.committeememberStremler, Mark A.en
dc.contributor.departmentEngineering Science and Mechanicsen
dc.date.accessioned2015-06-27T08:00:21Zen
dc.date.available2015-06-27T08:00:21Zen
dc.date.issued2015-06-26en
dc.description.abstractSlender 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.en
dc.description.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:5600en
dc.identifier.urihttp://hdl.handle.net/10919/53832en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectCatenaryen
dc.subjectStringen
dc.subjectTowingen
dc.subjectDynamical Systemen
dc.subjectPhase Portraiten
dc.subjectViscous Flowen
dc.titleCatenaries in Viscous Fluiden
dc.typeThesisen
thesis.degree.disciplineEngineering Mechanicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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