Bifurcation analysis of the structure of vortices in an uniform strain field.

Persistent Link:
http://hdl.handle.net/10150/184732
Title:
Bifurcation analysis of the structure of vortices in an uniform strain field.
Author:
Rajagopalan, Ramachandran.
Issue Date:
1989
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
We have studied the stationary solutions to the two-dimensional Euler's equation. A highly accurate scheme, based on boundary integral techniques was used in investigating these steady-state configurations. Bifurcation analysis on the solution of a uniform vortex patch in an externally applied strain field, yield new non-elliptical steady-state solutions apart from the elliptical structures reported by Moore & Saffman. The elliptical solutions correspond to the points on the primary solution branch and the non-elliptical solutions correspond to points on the bifurcation branches. We also observe the presence of a turning point indicating the finite resistance of these uniform vortices. Some of these new solutions suggest the possibility of coalescence between neighboring vortices. This leads to a new problem of considering a vortex pair in a strain field and computing their steady-state solutions. Numerical computations suggest that this guess is indeed correct, as we see the solution branch corresponding to the vortex pair intersect the bifurcation branch of the single vortex at a unique strain rate. Furthermore, looking at the profiles on the other bifurcation branches, it appears that merger of neighboring vortices is a recurring phenomenon.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Vortex-motion.; Fluid dynamics.; Bifurcation theory.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Applied Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Baker, Gregory

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleBifurcation analysis of the structure of vortices in an uniform strain field.en_US
dc.creatorRajagopalan, Ramachandran.en_US
dc.contributor.authorRajagopalan, Ramachandran.en_US
dc.date.issued1989en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractWe have studied the stationary solutions to the two-dimensional Euler's equation. A highly accurate scheme, based on boundary integral techniques was used in investigating these steady-state configurations. Bifurcation analysis on the solution of a uniform vortex patch in an externally applied strain field, yield new non-elliptical steady-state solutions apart from the elliptical structures reported by Moore & Saffman. The elliptical solutions correspond to the points on the primary solution branch and the non-elliptical solutions correspond to points on the bifurcation branches. We also observe the presence of a turning point indicating the finite resistance of these uniform vortices. Some of these new solutions suggest the possibility of coalescence between neighboring vortices. This leads to a new problem of considering a vortex pair in a strain field and computing their steady-state solutions. Numerical computations suggest that this guess is indeed correct, as we see the solution branch corresponding to the vortex pair intersect the bifurcation branch of the single vortex at a unique strain rate. Furthermore, looking at the profiles on the other bifurcation branches, it appears that merger of neighboring vortices is a recurring phenomenon.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectVortex-motion.en_US
dc.subjectFluid dynamics.en_US
dc.subjectBifurcation theory.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorBaker, Gregoryen_US
dc.contributor.committeememberDowney, Peteren_US
dc.contributor.committeememberLomen, Daviden_US
dc.contributor.committeememberCushing, Jamesen_US
dc.identifier.proquest8919054en_US
dc.identifier.oclc702459410en_US
All Items in UA Campus Repository are protected by copyright, with all rights reserved, unless otherwise indicated.