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The stability of body centered polygonal vortex line configurations Mertz, Gordon J.
Abstract
This thesis is concerned with the stability of rectilinear vortex line configurations. A method for consideration of stability problems, using the equations of motion for small perturbations about equilibrium, is developed; and the free energy criterion for stability stated. The former method is used in analyzing the stability of the body centered polygonal configuration, which is a Thomson polygon centered by a vortex of arbitrary relative circulation; the latter criterion is applied to the Thomson heptagon stability question. The main results are that a Thomson polygon of any order can be stabilized by a large enough central circulation and that the Thomson heptagon is stable.
Item Metadata
Title |
The stability of body centered polygonal vortex line configurations
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1977
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Description |
This thesis is concerned with the stability of rectilinear vortex line configurations. A method for consideration of stability problems, using the equations of motion for small perturbations about equilibrium, is developed; and the free energy criterion for stability stated. The former method is used in analyzing the stability of the body centered polygonal configuration, which is a Thomson polygon centered by a vortex of arbitrary relative circulation; the latter criterion is applied to the Thomson heptagon stability question. The main results are that a Thomson polygon of any order can be stabilized by a large enough central circulation and that the Thomson heptagon is stable.
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Genre | |
Type | |
Language |
eng
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Date Available |
2010-02-18
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0085746
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.