One approach to examining the stability of a fluid flow is to linearize the
evolution equation at an equilibrium and determine (if possible) the stability
of the resulting linear evolution equation. In this dissertation, the space of
perturbations of the equilibrium flow is split into two classes and growth of
the linear evolution operator on each class is analyzed. Our classification of
perturbations is most naturally described in V.I. Arnold’s geometric view of
fluid dynamics. The first class of perturbations we examine are those that
preserve the topology of vortex lines and the second class is the factor space
corresponding to the first class. In this dissertation we establish lower bounds
for the essential spectral radius of the linear evolution operator restricted to
each class of perturbations. / text
| Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/6571 |
| Date | 20 October 2009 |
| Creators | Thoren, Elizabeth Erin |
| Source Sets | University of Texas |
| Language | English |
| Detected Language | English |
| Format | electronic |
| Rights | Copyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works. |
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