Skip to main content
×
Home
    • Aa
    • Aa

Polygon formation and surface flow on a rotating fluid surface

  • R. BERGMANN (a1), L. TOPHØJ (a1), T. A. M. HOMAN (a1) (a2), P. HERSEN (a3), A. ANDERSEN (a1) and T. BOHR (a1)...
Abstract

We present a study of polygons forming on the free surface of a water flow confined to a stationary cylinder and driven by a rotating bottom plate as described by Jansson et al. (Phys. Rev. Lett., vol. 96, 2006, 174502). In particular, we study the case of a triangular structure, either completely ‘wet’ or with a ‘dry’ centre. For the dry structures, we present measurements of the surface shapes and the process of formation. We show experimental evidence that the formation can take place as a two-stage process: first the system approaches an almost stable rotationally symmetric state and from there the symmetry breaking proceeds like a low-dimensional linear instability. We show that the circular state and the unstable manifold connecting it with the polygon solution are universal in the sense that very different initial conditions lead to the same circular state and unstable manifold. For a wet triangle, we measure the surface flows by particle image velocimetry (PIV) and show that there are three vortices present, but that the strength of these vortices is far too weak to account for the rotation velocity of the polygon. We show that partial blocking of the surface flow destroys the polygons and re-establishes the rotational symmetry. For the rotationally symmetric state our theoretical analysis of the surface flow shows that it consists of two distinct regions: an inner, rigidly rotating centre and an outer annulus, where the surface flow is that of a point vortex with a weak secondary flow. This prediction is consistent with the experimentally determined surface flow.

Copyright
Corresponding author
Present address: Instrumentation and Controls Department, German–Dutch Wind Tunnels, Emmeloord, The Netherlands. Email address for correspondence: tbohr@fysik.dtu.dk
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

E. J. Hopfinger 1992 In Rotating Fluids in Geophysical and Industrial Applications (ed. E. J. Hopfinger ). Springer.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 21 *
Loading metrics...

Abstract views

Total abstract views: 81 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 27th March 2017. This data will be updated every 24 hours.