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N-VORTEX PROBLEM ON A ROTATING SPHERE
by
Houman Shokraneh
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MECHANICAL ENGINEERING)
December 2007
Copyright 2007 Houman Shokraneh
Object Description
| Title | N-vortex problem on a rotating sphere |
| Author | Shokraneh, Houman |
| Author email | hshokraneh@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Mechanical Engineering |
| School | Viterbi School of Engineering |
| Date defended/completed | 2007-07-17 |
| Date submitted | 2007 |
| Restricted until | Unrestricted |
| Date published | 2007-12-17 |
| Advisor (committee chair) | Newton, Paul K. |
| Advisor (committee member) |
Redekopp, Larry G. Ziane, Mohammed |
| Abstract | The evolution, interaction, and scattering of 2N-point vortices grouped into equal and opposite pairs (N-dipoles) on a rotating unit sphere is studied. A new coordinate system made up of the centers-of-vorticity and centroids associated with each dipole is introduced. With these coordinates, the nonlinear equations for an isolated dipole diagonalize and one directly obtains the equation for geodesic motion on the sphere for the dipole centroid. When two or more dipoles interact, the equations are viewed as an interacting billiard system on the sphere -- charged billiards -- with long range interactions causing the centroid trajectories to deviate from their geodesic paths. Canonical interactions are studied both with and without rotation. For two dipoles, the four basic interactions are described as exchange scattering, non-exchange scattering, loop scattering (head-on) and loop scattering (chasing) interactions. For three or more dipoles, one obtains a richer variety of interactions, although the interactions identified in the two-dipole case remain fundamental. |
| Keyword | N-vortex problem; dipole scattering; charged billiard equations |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Type | texts |
| Legacy record ID | usctheses-m985 |
| Rights | Shokraneh, Houman |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | http://www.usc.edu/isd/libraries/services/ask_a_librarian/email/ |
| Filename | etd-Shokraneh-20071217 |
| Archival file | uscthesesreloadpub_Volume14/etd-Shokraneh-20071217.pdf |
Description
| Title | Page 1 |
| Full text | N-VORTEX PROBLEM ON A ROTATING SPHERE by Houman Shokraneh A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (MECHANICAL ENGINEERING) December 2007 Copyright 2007 Houman Shokraneh |
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