Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published August 10, 2012 | Published
Journal Article Open

Perturbation response and pinch-off of vortex rings and dipoles


The nonlinear perturbation response of two families of vortices, the Norbury family of axisymmetric vortex rings and the Pierrehumbert family of two-dimensional vortex pairs, is considered. Members of both families are subjected to prolate shape perturbations similar to those previously introduced to Hill's spherical vortex, and their response is computed using contour dynamics algorithms. The response of the entire Norbury family to this class of perturbations is considered, in order to bridge the gap between past observations of the behaviour of thin-cored members of the family and that of Hill's spherical vortex. The behaviour of the Norbury family is contrasted with the response of the analogous two-dimensional family of Pierrehumbert vortex pairs. It is found that the Norbury family exhibits a change in perturbation response as members of the family with progressively thicker cores are considered. Thin-cored vortices are found to undergo quasi-periodic deformations of the core shape, but detrain no circulation into their wake. In contrast, thicker-cored Norbury vortices are found to detrain excess rotational fluid into a trailing vortex tail. This behaviour is found to be in agreement with previous results for Hill's spherical vortex, as well as with observations of pinch-off of experimentally generated vortex rings at long formation times. In contrast, the detrainment of circulation that is characteristic of pinch-off is not observed for Pierrehumbert vortex pairs of any core size. These observations are in agreement with recent studies that contrast the formation of vortices in two and three dimensions. We hypothesize that transitions in vortex formation, such as those occurring between wake shedding modes and in vortex pinch-off more generally, might be understood and possibly predicted based on the observed perturbation responses of forming vortex rings or dipoles.

Additional Information

© 2012 Cambridge University Press. Received 7 November 2011; revised 11 May 2012; accepted 17 May 2012; first published online 29 June 2012. This work was funded by an NSF Graduate Research Fellowship to C.O'F., and by Office of Naval Research awards N000140810918 and N000141010137 to J.O.D. The authors would like to thank Professor T. Leonard for the many helpful discussions on the axisymmetric contour dynamics formulation.

Attached Files

Published - OFarrell2012p19189J_Fluid_Mech.pdf


Files (952.9 kB)
Name Size Download all
952.9 kB Preview Download

Additional details

August 19, 2023
October 18, 2023