Polygon formation and surface flow on a rotating fluid surface
Bergmann, R. and Tophoj, L. and Homan, T.A.M. and Hersen, P. and Andersen, A. and Bohr, T. (2011) Polygon formation and surface flow on a rotating fluid surface. Journal of fluid mechanics, 679 . pp. 415431. ISSN 00221120

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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 twostage process: first the system approaches an almost stable rotationally symmetric state and from there the symmetry breaking proceeds like a lowdimensional 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 reestablishes 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 
Item Type:  Article 
Copyright:  © Cambridge University Press 
Faculty:  Science and Technology (TNW) 
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Link to this item:  http://purl.utwente.nl/publications/79041 
Official URL:  http://dx.doi.org/10.1017/jfm.2011.152 
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