Experimental Confirmation of Kelvin’s Equilibria

Georgios H. Vatistas, Hamid A. Abderrahmane, and M. H. Kamran Siddiqui
Phys. Rev. Lett. 100, 174503 – Published 30 April 2008

Abstract

We experimentally corroborate the core analytical deductions of Thomson’s 124-year-old theorem, vis-à-vis the stability of a ring of N vortices. Observations made in water vortices produced inside a cylinder via a revolving disk confirm that the regular N-gons are stable for N6 and unstable for N8. The N6 equilibria are exceptionally resilient. When destroyed, they reemerge in their original form. We reason that the heptagonal system either survives in an exceedingly narrow band of disk speeds or is in theory critically stable. Contrary to the results with a rotating bottom reported by Jansson et al. [Phys. Rev. Lett. 96, 174502 (2006)], we show the interfacial axial symmetry does not break spontaneously but through spectral development, the functional relationship amongst the polygon rotation and disk speed is surprisingly simple, and the pattern to disk frequency ratio depends on both Froude and wave numbers.

  • Figure
  • Figure
  • Figure
  • Received 25 October 2007

DOI:https://doi.org/10.1103/PhysRevLett.100.174503

©2008 American Physical Society

Authors & Affiliations

Georgios H. Vatistas*, Hamid A. Abderrahmane, and M. H. Kamran Siddiqui

  • Department of Mechanical and Industrial Engineering, Concordia University, Montreal H3G 1M8, Canada

  • *Corresponding author. vatistas@encs.concordia.ca

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 100, Iss. 17 — 2 May 2008

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review Letters

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×