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Classification of instability modes in a model of aluminium reduction cells with a uniform magnetic field
journal contribution
posted on 2015-03-10, 12:19 authored by Sergei Molokov, Gennady El, Alexander LukyanovA unified view on the interfacial instability in a model of aluminium reduction cells in the presence of a uniform, vertical, background magnetic field is presented. The classification of instability modes is based on the asymptotic theory for high values of parameter β, which characterises the ratio of the Lorentz force based on the disturbance current, and gravity. It is shown that the spectrum of the travelling waves consists of two parts independent of the horizontal cross-section of the cell: highly unstable wall modes and stable or weakly unstable centre, or Seles modes. The wall modes with the disturbance of the interface being localised at the sidewalls of the cell dominate the dynamics of instability. Seles modes are characterised by a distributed disturbance over the whole horizontal extent of the cell. As β increases these modes are stabilized by the field.
History
School
- Science
Department
- Mathematical Sciences
Published in
Theoretical and Computational Fluid DynamicsVolume
25Issue
5Pages
261 - 279Citation
MOLOKOV, S., EL, G.A. and LUKYANOV, A., 2011. Classification of instability modes in a model of aluminium reduction cells with a uniform magnetic field. Theoretical and Computational Fluid Dynamics, 25 (5), pp. 261-279.Publisher
© Springer-VerlagVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2011Notes
The final publication is available at Springer via http://dx.doi.org/10.1007/s00162-010-0201-yISSN
0935-4964eISSN
1432-2250Publisher version
Language
- en