Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-28T07:30:51.326Z Has data issue: false hasContentIssue false
  • English
  • Français

Waves and instabilities in rotating free surfaceflows

Published online by Cambridge University Press:  22 May 2014

J. Mougel ,
D. Fabre  and
L. Lacaze
J. Mougel*
Affiliation:
Institut de Mécanique des Fluides de Toulouse, UMR CNRS/INPT/UPS 5502, Allée Camille Soula, 31400 Toulouse, France
D. Fabre
Affiliation:
Institut de Mécanique des Fluides de Toulouse, UMR CNRS/INPT/UPS 5502, Allée Camille Soula, 31400 Toulouse, France
L. Lacaze
Affiliation:
Institut de Mécanique des Fluides de Toulouse, UMR CNRS/INPT/UPS 5502, Allée Camille Soula, 31400 Toulouse, France CNRS, IMFT, 31400 Toulouse, France
*
a Corresponding author:jerome.mougel@imft.fr
Get access

Abstract

The stability properties of the rotating free surface flow in a cylindrical container isstudied using a global stability approach, considering successively three models. For thecase of solid body rotation (Newton’s bucket), all eigenmodes are found to be stable, andare classified into three families: gravity waves, singular inertial modes, and Rossbywaves. For the case of a potential flow, an instability is found. The mechanism isexplained as a resonance between gravity waves and centrifugal waves, and is thought to beat the origin of the “rotating polygon instability” observed in experiments where the flowis driven by rotation of the bottom plate (see L. Tophøj, J. Mougel, T. Bohr, D. Fabre,The Rotating Polygon Instability of a Swirling Free Surface Flow, Phys. Rev. Lett. 110(2013) 194502). Finally, in the case of the Rankine vortex which in fact consists in thecombination of the two first cases, we report a new instability mechanism involving Rossbyand gravity waves.

Keywords

rotating flowswavesinstabilities
Type
Research Article
Information
Mechanics & Industry , Volume 15 , Issue 2 , 2014 , pp. 107 - 112
Copyright
© AFM, EDP Sciences 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Tophøj, L., Mougel, J., Bohr, T., Fabre, D., The Rotating Polygon Instability of a Swirling Free Surface Flow, Phys. Rev. Lett. 110 (2013) 194502 CrossRefGoogle ScholarPubMed
G.H. Vatistas, A note on liquid vortex sloshing and Kelvin’s equilibria, J. Fluid Mech. (1990) 241–248
Bergmann, R., Tophøj, L., Homan, T.A.M., Hersen, P., Andersen, A., Bohr, T., Polygon formation and surface flow on a rotating fluid surface, J. Fluid Mech. 679 (2011) 415–431 CrossRefGoogle Scholar
K. Iga, S. Yokota, S. Watanabe, T.H. Niino Ikeda, N. Misawa, Submitted to Fluid Dyn. Res. (2014)
Jansson, T.R.N., Haspang, M.P., Jensen, K.H., Bohr, T., Polygons on a Rotating Fluid Surface, Phys. Rev. Lett. 96 (2006) 174502 CrossRefGoogle ScholarPubMed
Suzuki, T., Iima, M., Hayase, Y., Surface switching of rotating fluid in a cylinder, Phys. Fluids 18 (2006) 101701 CrossRefGoogle Scholar
Rieutord, M., Valdettaro, L., Inertial waves in a rotating spherical shell, J. Fluid Mech. 341 (1997) 77–99 CrossRefGoogle Scholar
J. Mougel, Étude de stabilité linéaire du seau de Newton, Mémoire de stage de Master, ISAE, 2011
Hecht, F., New development in freefem++, J. Numer. Math. 20 (2012) 251–265 CrossRefGoogle Scholar
H.P. Greenspan, The theory of rotating flows, Cambridge Univ. Press (1969)
R.A. Ibrahim, Liquid Sloshing Dynamics, Theory and Applications, Cambridge Univ. Press (2005)
Cairns, R.A., The role of negative energy waves in some instabilities of parallel flows, J. Fluid Mech. 92 (1979) 1–14 CrossRefGoogle Scholar
D. Fabre, J. Mougel, Generation of tree-dimensional patterns through wave interaction in a model of free surface swirling flow, Accepted for publication in Fluid Dyn. Res. (2014)
P.G. Saffman, Vortex Dynamics, Cambridge Univ. Press, 1992