Theoretical analyses of vortex wake stability

Jetting swimmers, such as squid or jellyfish, propel themselves by forming axisymmetric vortex rings. In order to evaluate the performance of these swimmers, it is necessary to assess the optimality of the vortex wakes they produce, which requires an understanding of their stability. In this project, we consider the Norbury family of vortices as a model for the vortex rings produced by jetting swimmers. Previous research has studied the stability of Hill's spherical vortex under axisymmetric prolate and oblate shape perturbations. However, the stability of other members of the Norbury family to axisymmetric perturbations of the type that might occur during the vortex formation process in jetting swimmers is unknown. In order to assess the stability of different members of the family, we introduce physically pertinent shape perturbations and simulate their development using a contour dynamics approach.

Publications

  • C. O'Farrell and J. O. Dabiri (2012). "Perturbation response and pinch-off of vortex rings and dipoles", Journal of Fluid Mechanics, Vol. 704, pp. 280-300
  • C. O'Farrell and J. O. Dabiri (2011). "Vortex 'pinch-off' in the Norbury and Pierrehumbert families of vortices", Workshop on Coherent Structures in Dynamical Systems. Lorentz Center, Universiteit Leiden, The Netherlands May 16-20
  • C. O'Farrell and J. O. Dabiri (2011). "Vortex 'pinch-off' in the Norbury family of vortices", Southern California Symposium on Flow Physics, University of Southern California, April 16.
  • C. O'Farrell and J. O. Dabiri (2010). "The stability of a family of vortex rings", Bulletin of the American Physical Society Division of Fluid Dynamics Meeting. November 21-23, Long Beach, CA.