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A Dynamical Systems Analysis of Vortex Pinch-Off


O'Farrell, Clara (2013) A Dynamical Systems Analysis of Vortex Pinch-Off. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/AFAA-KF43.


Vortex rings constitute the main structure in the wakes of a wide class of swimming and flying animals, as well as in cardiac flows and in the jets generated by some moss and fungi. However, there is a physical limit, determined by an energy maximization principle called the Kelvin-Benjamin principle, to the size that axisymmetric vortex rings can achieve. The existence of this limit is known to lead to the separation of a growing vortex ring from the shear layer feeding it, a process known as `vortex pinch-off', and characterized by the dimensionless vortex formation number. The goal of this thesis is to improve our understanding of vortex pinch-off as it relates to biological propulsion, and to provide future researchers with tools to assist in identifying and predicting pinch-off in biological flows.

To this end, we introduce a method for identifying pinch-off in starting jets using the Lagrangian coherent structures in the flow, and apply this criterion to an experimentally generated starting jet. Since most naturally occurring vortex rings are not circular, we extend the definition of the vortex formation number to include non-axisymmetric vortex rings, and find that the formation number for moderately non-axisymmetric vortices is similar to that of circular vortex rings. This suggests that naturally occurring vortex rings may be modeled as axisymmetric vortex rings. Therefore, we consider the perturbation response of the Norbury family of axisymmetric vortex rings. This family is chosen to model vortex rings of increasing thickness and circulation, and their response to prolate shape perturbations is simulated using contour dynamics. Finally, the response of more realistic models for vortex rings, constructed from experimental data using nested contours, to perturbations which resemble those encountered by forming vortices more closely, is simulated using contour dynamics. In both families of models, a change in response analogous to pinch-off is found as members of the family with progressively thicker cores are considered. We posit that this analogy may be exploited to understand and predict pinch-off in complex biological flows, where current methods are not applicable in practice, and criteria based on the properties of vortex rings alone are necessary.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Fluid mechanics, vortex dynamics, biological propulsion, Lagrangian coherent structures, contour dynamics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Control and Dynamical Systems
Minor Option:Aeronautics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Dabiri, John O.
Thesis Committee:
  • Dabiri, John O. (chair)
  • Leonard, Anthony
  • Gharib, Morteza
  • Murray, Richard M.
  • Doyle, John Comstock
Defense Date:29 April 2013
Funding AgencyGrant Number
NSF Graduate Research FellowshipUNSPECIFIED
Office of Naval Research N000140810918
Office of Naval Research N000141010137
Betty and Gordon Moore FoundationUNSPECIFIED
Record Number:CaltechTHESIS:05032013-161632237
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for ch. 2 adapted for ch. 4
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7665
Deposited By: Clara O'Farrell
Deposited On:02 May 2014 16:14
Last Modified:26 Oct 2023 23:12

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