## Polygon formation and surface flow on a rotating fluid surface

Publication: Research - peer-review › Journal article – Annual report year: 2011

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**Polygon formation and surface flow on a rotating fluid surface.** / Bergmann, Raymond; Tophøj, Laust Emil Hjerrild; Homan, T. A. M.; Hersen, P.; Andersen, Anders Peter; Bohr, Tomas.

Publication: Research - peer-review › Journal article – Annual report year: 2011

### Harvard

*Journal of Fluid Mechanics*, vol 679, pp. 415-431., 10.1017/jfm.2011.152

### APA

*Journal of Fluid Mechanics*,

*679*, 415-431. 10.1017/jfm.2011.152

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### MLA

*Journal of Fluid Mechanics*. 2011, 679. 415-431. Available: 10.1017/jfm.2011.152

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### Bibtex

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### RIS

TY - JOUR

T1 - Polygon formation and surface flow on a rotating fluid surface

A1 - Bergmann,Raymond

A1 - Tophøj,Laust Emil Hjerrild

A1 - Homan,T. A. M.

A1 - Hersen,P.

A1 - Andersen,Anders Peter

A1 - Bohr,Tomas

AU - Bergmann,Raymond

AU - Tophøj,Laust Emil Hjerrild

AU - Homan,T. A. M.

AU - Hersen,P.

AU - Andersen,Anders Peter

AU - Bohr,Tomas

PB - Cambridge University Press

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

KW - Waves/free-surface flows

KW - Vortex flows

KW - Rotating flows

UR - http://www.cambridge.org/

U2 - 10.1017/jfm.2011.152

DO - 10.1017/jfm.2011.152

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

VL - 679

SP - 415

EP - 431

ER -