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Dynamics of flow structures and surface shapes in the surface switching of rotating fluid

Published online by Cambridge University Press:  21 January 2016

M. Iima  and
Y. Tasaka
M. Iima*
Affiliation:
Graduate School of Science, Hiroshima University, 1-7-1, Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8521, Japan
Y. Tasaka
Affiliation:
Laboratory for Flow Control, Hokkaido University, N13W8, Sapporo 060-8628, Japan
*
†Email address for correspondence: [email protected]
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Abstract

We present a study of the dynamics of the free-surface shape of a flow in a cylinder driven by a rotating bottom. Near the critical Reynolds number of the laminar–turbulent transition of the boundary layer, the free surface exhibits irregular surface switching between axisymmetric and non-axisymmetric shapes, and the switching often occurs with a significant change in the free-surface height. Although such surface deformation is known to be caused by the flow structures, the detailed flow structures of a rotating fluid with a large surface deformation have yet to be analysed. We thus investigate the velocity distribution and surface shape dynamics and show that the flow field during the loss of its axisymmetry is similar to that predicted by the theory of Tophøj et al. (Phys. Rev. Lett., vol. 110, 2013, 194502). The slight difference observed by quantitative comparison is caused by the fact that the basic flow of our study contains a weak rigid-body rotation in addition to the potential flow assumed by the theory. Furthermore, the observed non-axisymmetric surface shape, which has an elliptic horizontal cross-section, is generally associated with a quadrupole vortex structure. It is also found that the relative position between the free surface and the flow structure changes before and after the detachment of the free surface from the bottom. The change just after the detachment is drastic and occurs via a transient dipole-like vortex structure.

JFM classification

Instability: Instability Vortex Flows: Vortex Flows Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 789 , 25 February 2016 , pp. 402 - 424
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Copyright
© 2016 Cambridge University Press 

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References

Ait Abderrahmane, H., Siddiqui, K., Vatistas, G. H., Fayed, M. & Ng, H. D. 2011 Symmetrization of a polygonal hollow-core vortex through beat-wave resonance. Phys. Rev. E 83 (5), 056319.Google ScholarPubMed
Bach, B., Linnartz, E. C., Vested, M. H., Andersen, A. & Bohr, T. 2014 From Newton’s bucket to rotating polygons: experiments on surface instabilities in swirling flows. J. Fluid Mech. 759, 386–403.CrossRefGoogle Scholar
Bergmann, R., Tophoj, L., Homan, T. A. M., Hersen, P., Andersen, A. & Bohr, T. 2011 Polygon formation and surface flow on a rotating fluid surface. J. Fluid Mech. 679, 415–431.CrossRefGoogle Scholar
Bouffanais, R. & Jacono, D. L. 2009 Unsteady transitional swirling flow in the presence of a moving free surface. Phys. Fluids 21, 064107.CrossRefGoogle Scholar
Fabre, D. & Mougel, J. 2014 Generation of three-dimensional patterns through wave interaction in a model of free surface swirling flow. Fluid Dyn. Res. 46, 061415.CrossRefGoogle Scholar
Fujimoto, S. & Takeda, Y. 2009 Topology changes of the interface between two immiscible liquid layers by a rotating lid. Phys. Rev. E 80, 015304(R).Google ScholarPubMed
Iga, K., Yokota, S., Watanabe, S., Ikeda, T., Niino, H. & Misawa, N. 2014 Various phenomena on a water vortex in a cylindrical tank over a rotating bottom. Fluid Dyn. Res. 46 (3), 031409.CrossRefGoogle Scholar
Iima, M., Iijima, Y., Sato, Y. & Tasaka, Y. 2011 A time-series analysis of the free-surface motion of rotational flow. Theor. Appl. Mech. Japan 59, 187–193.Google Scholar
Jansson, T. R. N., Haspang, M. P., Jensen, K. H., Hersen, P. & Bohr, T. 2006 Polygons on a rotating fluid surface. Phys. Rev. Lett. 96, 174502.CrossRefGoogle ScholarPubMed
Kahouadji, L. & Witkowski, L. M. 2014 Free surface due to a flow driven by a rotating disk inside a vertical cylindrical tank: axisymmetric configuration. Phys. Fluids 26 (7), 072105.CrossRefGoogle Scholar
Lopez, J. M., Marques, F., Hirsa, A. H. & Miraghaie, R. 2004 Symmetry-breaking in free-surface cylinder flows. J. Fluid Mech. 502, 99–126.CrossRefGoogle Scholar
Mougel, J., Fabre, D. & Lacaze, L. 2014 Waves and instabilities in rotating free surface flows. Mech. Ind. 15 (2), 107–112.CrossRefGoogle Scholar
Murai, Y., Tasaka, Y., Nambu, Y., Takeda, Y. & Gonzalez, R. 2010 Ultrasonic detection of moving interfaces in gas–liquid two-phase flow. Flow Meas. Instrum. 21, 356–366.CrossRefGoogle Scholar
Sato, Y., Iima, M. & Tasaka, Y. 2011 Random dynamics from a time series of rotating fluid. Hokkaido University Preprint Series in Mathematics, No. 979.Google Scholar
Suzuki, T., Iima, M. & Hayase, Y. 2006 Surface switching of rotating fluid in a cylinder. Phys. Fluids 18, 101701.CrossRefGoogle Scholar
Tasaka, Y. & Iima, M. 2009 Flow transitions in the surface switching of rotating fluid. J. Fluid. Mech. 636, 475–484.CrossRefGoogle Scholar
Tasaka, Y., Iima, M. & Ito, K. 2008a Rotataing flow transition related to surface switching. J. Phys.: Conf. Ser. 137, 12030.Google Scholar
Tasaka, Y., Ito, K. & Iima, M. 2008b Visualization of a rotating flow under large-deformed free surface using anisotropic flakes. J. Vis. 11, 163–172.Google Scholar
Tophøj, L., Mougel, J., Bohr, T. & Fabre, D. 2013 Rotating polygon instability of a swirling free surface flow. Phys. Rev. Lett. 110 (19), 194502.CrossRefGoogle ScholarPubMed
Vatistas, G. H. 1990 A note on liquid vortex sloshing and Kelvin’s equilibria. J. Fluid. Mech. 217, 241–248.CrossRefGoogle Scholar
Vatistas, G. H., Abderrahmane, H. A. & Siddqui, H. M. K. 2008 Experimental confirmation of Kelvin’s equilibrium. Phys. Rev. Lett. 100, 174503.CrossRefGoogle Scholar