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Shape and Stability of Two-Dimensional Uniform Vorticity Regions


Kamm, James Russell (1987) Shape and Stability of Two-Dimensional Uniform Vorticity Regions. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/NW61-5178.


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 and 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 and 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 and 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 Jiménez [1986b] by showing that the characteristic subharmonic stability "cross" persists for vortex streets of finite but unequal areas.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Bifurcation; Schwarz function; stability; vorticity
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Saffman, Philip G.
Thesis Committee:
  • Saffman, Philip G. (chair)
  • Keller, Herbert Bishop
  • Kubota, Toshi
  • Leonard, Anthony
  • Wiggins, Stephen R.
Defense Date:28 April 1987
Non-Caltech Author Email:kammj (AT)
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-79-C-0412
Office of Naval Research (ONR)N00014-85-K-0205
Department of Energy (DOE)DE-AA03-76SF00767
Max Planck Institute for Dynamics and Self-Organization315-402-093-6
Record Number:CaltechETD:etd-06302004-093810
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2782
Deposited By: Imported from ETD-db
Deposited On:30 Jun 2004
Last Modified:21 Dec 2019 03:59

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