Catenaries in Viscous Fluid

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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Engineering Mechanics

Department dc:contributor.department

Engineering Science and Mechanics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2015

Author dc:creator

• Chakrabarti, Brato

Chair dc:contributor.committeechair

• Hanna, James

Committee members dc:contributor.committeemember

• Ross, Shane D.
• Stremler, Mark A.

• Catenary
• String
• Towing
• Dynamical System
• Phase Portrait
• Viscous Flow

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:5600

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/53832