Skip to main content

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

  • M. Iima (a1) and Y. Tasaka (a2)

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.

Corresponding author
Email address for correspondence:
Hide All
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.
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, 386403.
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, 415431.
Bouffanais, R. & Jacono, D. L. 2009 Unsteady transitional swirling flow in the presence of a moving free surface. Phys. Fluids 21, 064107.
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.
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).
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.
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, 187193.
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.
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.
Lopez, J. M., Marques, F., Hirsa, A. H. & Miraghaie, R. 2004 Symmetry-breaking in free-surface cylinder flows. J. Fluid Mech. 502, 99126.
Mougel, J., Fabre, D. & Lacaze, L. 2014 Waves and instabilities in rotating free surface flows. Mech. Ind. 15 (2), 107112.
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, 356366.
Sato, Y., Iima, M. & Tasaka, Y. 2011 Random dynamics from a time series of rotating fluid. Hokkaido University Preprint Series in Mathematics, No. 979.
Suzuki, T., Iima, M. & Hayase, Y. 2006 Surface switching of rotating fluid in a cylinder. Phys. Fluids 18, 101701.
Tasaka, Y. & Iima, M. 2009 Flow transitions in the surface switching of rotating fluid. J. Fluid. Mech. 636, 475484.
Tasaka, Y., Iima, M. & Ito, K. 2008a Rotataing flow transition related to surface switching. J. Phys.: Conf. Ser. 137, 12030.
Tasaka, Y., Ito, K. & Iima, M. 2008b Visualization of a rotating flow under large-deformed free surface using anisotropic flakes. J. Vis. 11, 163172.
Tophøj, L., Mougel, J., Bohr, T. & Fabre, D. 2013 Rotating polygon instability of a swirling free surface flow. Phys. Rev. Lett. 110 (19), 194502.
Vatistas, G. H. 1990 A note on liquid vortex sloshing and Kelvin’s equilibria. J. Fluid. Mech. 217, 241248.
Vatistas, G. H., Abderrahmane, H. A. & Siddqui, H. M. K. 2008 Experimental confirmation of Kelvin’s equilibrium. Phys. Rev. Lett. 100, 174503.
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? *



Full text views

Total number of HTML views: 2
Total number of PDF views: 73 *
Loading metrics...

Abstract views

Total abstract views: 203 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 20th March 2018. This data will be updated every 24 hours.