Polygonal Vortexes

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Photo by G. Vatistas


Copyright Institute of Physics and IOP Publishing 2009

Polar vortex replicated in a bucket

By Hamish Johnston, editor of physicsworld.com

Source: http://physicsworld.com/cws/article/news/2008/may/08/polar-vortex-replicated-in-a-bucket

May 8, 2008
While it might seem strange that a circular vortex will suddenly develop corners, this curious behaviour was first hinted at over a century ago by the British physicist J J Thomson. Working on the now long-abandoned theory of “vortex atoms”, which assumed that each atom is a vortex in the ether, Thomson calculated that when a single vortex reaches a critical angular velocity, it will split into two vortices that orbit each other, making a diatomic molecule.
As the angular velocity increased further, Thomson predicted that the system would separate into three, four, five and six vortices, creating larger molecules. This idea of multiple vortices was largely forgotten until 1979, when Richard Packard and colleagues at the University of California, Berkeley saw as many as 11 vortices in a rotating cylinder of superfluid helium (Phys Rev Lett 43 214).

Retrieved by DonEMitchell 08:56, 21 June 2012 (MDT) from http://physicsworld.com/cws/article/news/2008/may/08/polar-vortex-replicated-in-a-bucket

PRL 98, 049901 (2007)      week ending 26 JANUARY 2007

Erratum: Polygons on a Rotating Fluid Surface
[Phys. Rev. Lett. 96, 174502 (2006)]

Thomas R. N. Jansson, Martin P. Haspang, Kare H. Jensen, Pascal Hersen, and Tomas Bohr
(Received 20 December 2006; published 24 January 2007)

DOI: 10.1103/PhysRevLett.98.049901 PACS numbers: 47.20.Ky, 47.32.C , 47.32.Ef, 99.10.Cd

In our recent Letter [1] we describe an unexpected instability of a rotating fluid, leading to rotating polygonal deformations of the surface. We were unaware that such states had been observed in similar experiments 16 years earlier and were described in the series of papers by G. H. Vatistas and collaborators; see Refs. [2– 5]. We are embarrassed not to have found these references in our extensive literature search (which obviously did not include the term ‘‘Kelvin’s equilibria’’), but we are happy to have drawn attention to an important unexplained fluid instability.
[1] T. R. N. Jansson, M. P. Haspang, K. H. Jensen, P. Hersen, and T. Bohr, Phys. Rev. Lett. 96, 174502 (2006).
[2] G. H. Vatistas, J. Fluid Mech. 217, 241 (1990).
[3] G. H. Vatistas, J. Wang, and S. Lin, J. Exp. Fluids 13, 377 (1992).
[4] G. H. Vatistas, J. Wang, and S. Lin, Acta Mech. 103, 89 (1994).
[5] G. H. Vatistas, N. Esmail, and C. Ravanis, 39th AIAA Aerospace Sciences Meeting and Exhibit, 8-11 January 2001, Reno, NV, Paper No. AIAA 2001-0168.

0031-9007/07/98(4)/049901(1) 049901-1         © 2007 The American Physical Society

Retrieved by DonEMitchell 09:19, 21 June 2012 (MDT) from http://prl.aps.org/abstract/PRL/v98/i4/e049901

Cambridge Journal of Fluid Mechanics
(2004), 502 : pp 99-126

Copyright © 2004 Cambridge University Press
DOI: http://dx.doi.org/10.1017/S0022112003007481 (About DOI)
Published online: 01 March 2004

Symmetry breaking in free-surface cylinder flows


a1 Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, USA
a2 Departament de Física Aplicada, Universitat Politècnica de Catalunya, Jordi Girona Salgado s/n, Mòdul B4 Campus Nord, 08034 Barcelona, Spain
a3 Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA


The flow in a stationary open cylinder driven by the constant rotation of the bottom endwall is unstable to three-dimensional perturbations for sufficiently large rotation rates. The bifurcated state takes the form of a rotating wave. Two distinct physical mechanisms responsible for the symmetry breaking are identified, which depend on whether the fluid depth is sufficiently greater or less than the cylinder radius. For deep systems, the rotating wave results from the instability of the near-wall jet that forms as the boundary layer on the rotating bottom endwall is turned into the interior. In this case the three-dimensional perturbations vanish at the air/water interface. On the other hand, for shallow systems, the fluid at radii less than about half the cylinder radius is in solid-body rotation whereas the fluid at larger radii has a strong meridional circulation. The interface between these two regions of flow is unstable to azimuthal disturbances and the resulting rotating wave persists all the way to the air/water interface. The flow dynamics are explored using three-dimensional Navier–Stokes computations and experimental results obtained via digital particle image velocimetry. The use of a flat stress-free model for the air/water interface reproduces the experimental results in the deep system but fails to capture the primary instability in the shallow system, even though the experimental imperfections, i.e. departures from a perfectly flat and clean air/water interface, are about the same for the deep and the shallow systems. The flat stress-free model boundary conditions impose a parity condition on the numerical solutions, and the consideration of an extended problem which reveals this hidden symmetry provides insight into the symmetry-breaking instabilities.
(Received April 22 2003)
(Revised October 6 2003)

Retrieved by DonEMitchell 08:44, 21 June 2012 (MDT) from http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=206031

See also