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Type of Document	Dissertation
Author	Kamm, James Russell
Author's Email Address	kammj AT lanl.gov
URN	etd-06302004-093810
Persistent URL	http://resolver.caltech.edu/CaltechETD:etd-06302004-093810
Title	Shape and stability of two-dimensional uniform vorticity regions
Degree	PhD
Option	Applied Mathematics
Advisory Committee	Advisor Name Title P.G. Saffman Committee Chair
Keywords	Schwarz function bifurcation stability vorticity
Date of Defense	1987-04-28
Availability	unrestricted
Abstract The steady shapes, linear stability, and energetics of regions of uniform, constant vorticity in an incompressible, inviscid fluid are investigated. The method of Schwarz functions as introduced by Meiron, Saffman & Schatzman [1984] is used in the mathematical formulation of these problems. Numerical and analytical analyses are provided for several configurations. For the single vortex in strained and rotating flow fields, we find new solutions that bifurcate from the branch of steady elliptical solutions. These nonelliptical steady states are determined to be linearly unstable. We examine the corotating vortex pair and numerically confirm the theoretical results of Saffman & Szeto [1980], relating linear stability characteristics to energetics. The stability properties of the infinite single array of vortices are quantified. The pairing instability is found to be the most unstable subharmonic disturbance, and the existence of an area-dependent superharmonic instability (Saffman & Szeto [1981]) is numerically confirmed. These results are exhibited qualitatively by an elliptical vortex model. Lastly, we study the effects of unequal area on the stability of the infinite staggered double array of vortices. We numerically verify the results of the perturbation analysis of Jimenez [1986b] by showing that the characteristic subharmonic stability "cross" persists for vortex streets of finite but unequal areas.
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