New experimental confirmation of Kelvin’s equilibria

  • Hamid Ait AbderrahmaneEmail author
  • Mohamed Fayed
  • Hoi Dick Ng
  • Georgios H. Vatistas
Regular Article


This paper deals with the polygonal patterns observed within the hollow core vortex generated in viscous fluid by a rotating disc at the bottom of a cylindrical container. The role of the working fluid viscosity, which is varied in the interval of 1–22 times that of water, was investigated. The results show that the rotating frequency of the polygonal patterns remains locked at 0.13 the rotating disc’s frequency. The results provide new evidence that the polygonal patterns are an inviscid-like (potential flow) phenomenon, due to satellites “point vortices” at their corners orbiting a central vortex. The results provide new evidence in support of the hypothesis that the satellite vortex assembly, fixed at the corners of regular polygons and orbiting in unison around the central vortex could be viewed approximately as a slightly viscous potential flow phenomenon. These give also credence to our previous conjecture that the transition between two subsequent patterns is analogous to “Landau damping” in plasma physics.


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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Hamid Ait Abderrahmane
    • 1
    Email author
  • Mohamed Fayed
    • 2
  • Hoi Dick Ng
    • 3
  • Georgios H. Vatistas
    • 3
  1. 1.Khalifa University of Science and Technology, Masdar InstituteMasdar City, Abu DhabiUnited Arab Emirates
  2. 2.Mechanical Engineering Department, Faculty of EngineeringAlexandria UniversityAlexandriaEgypt
  3. 3.Department of Mechanical and Industrial EngineeringConcordia UniversityMontrealCanada

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