Eur. Phys. J. Plus (2018) 133: 339
https://doi.org/10.1140/epjp/i2018-12188-5

Regular Article

New experimental confirmation of Kelvin’s equilibria

¹ Khalifa University of Science and Technology, Masdar Institute, P.O. Box 54224, Masdar City, Abu Dhabi, United Arab Emirates
² Mechanical Engineering Department, Faculty of Engineering, Alexandria University, Alexandria, Egypt
³ Department of Mechanical and Industrial Engineering, Concordia University, Montreal, Canada

^* e-mail: habderrahmane@masdar.ac.ae

Received: 6 February 2017
Accepted: 11 July 2018
Published online: 27 August 2018

Abstract

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.