Polygon formation and surface flow on a rotating fluid surface

R.P.H.M. Bergmann, R. Bergmann, L. Tophoj, T.A.M. Homan, T.A.M. Homan, P. Hersen, A. Andersen, T. Bohr

Research output: Contribution to journalArticleAcademicpeer-review

39 Citations (Scopus)

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
Original languageUndefined
Pages (from-to)415-431
Number of pages17
JournalJournal of fluid mechanics
Volume679
DOIs
Publication statusPublished - 2011

Keywords

  • waves/free-surface flows
  • vortex flows
  • METIS-277993
  • Rotating flows
  • IR-79041

Cite this

Bergmann, R. P. H. M., Bergmann, R., Tophoj, L., Homan, T. A. M., Homan, T. A. M., Hersen, P., ... Bohr, T. (2011). Polygon formation and surface flow on a rotating fluid surface. Journal of fluid mechanics, 679, 415-431. https://doi.org/10.1017/jfm.2011.152
Bergmann, R.P.H.M. ; Bergmann, R. ; Tophoj, L. ; Homan, T.A.M. ; Homan, T.A.M. ; Hersen, P. ; Andersen, A. ; Bohr, T. / Polygon formation and surface flow on a rotating fluid surface. In: Journal of fluid mechanics. 2011 ; Vol. 679. pp. 415-431.
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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 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",
keywords = "waves/free-surface flows, vortex flows, METIS-277993, Rotating flows, IR-79041",
author = "R.P.H.M. Bergmann and R. Bergmann and L. Tophoj and T.A.M. Homan and T.A.M. Homan and P. Hersen and A. Andersen and T. Bohr",
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Bergmann, RPHM, Bergmann, R, Tophoj, L, Homan, TAM, Homan, TAM, Hersen, P, Andersen, A & Bohr, T 2011, 'Polygon formation and surface flow on a rotating fluid surface', Journal of fluid mechanics, vol. 679, pp. 415-431. https://doi.org/10.1017/jfm.2011.152

Polygon formation and surface flow on a rotating fluid surface. / Bergmann, R.P.H.M.; Bergmann, R.; Tophoj, L.; Homan, T.A.M.; Homan, T.A.M.; Hersen, P.; Andersen, A.; Bohr, T.

In: Journal of fluid mechanics, Vol. 679, 2011, p. 415-431.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

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

AU - Bergmann, R.P.H.M.

AU - Bergmann, R.

AU - Tophoj, L.

AU - Homan, T.A.M.

AU - Homan, T.A.M.

AU - Hersen, P.

AU - Andersen, A.

AU - Bohr, T.

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 - METIS-277993

KW - Rotating flows

KW - IR-79041

U2 - 10.1017/jfm.2011.152

DO - 10.1017/jfm.2011.152

M3 - Article

VL - 679

SP - 415

EP - 431

JO - Journal of fluid mechanics

JF - Journal of fluid mechanics

SN - 0022-1120

ER -

Bergmann RPHM, Bergmann R, Tophoj L, Homan TAM, Homan TAM, Hersen P et al. Polygon formation and surface flow on a rotating fluid surface. Journal of fluid mechanics. 2011;679:415-431. https://doi.org/10.1017/jfm.2011.152