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Generalized hydrodynamic reductions of the kinetic equation for a soliton gas

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posted on 10.03.2015 by Maxim V. Pavlov, Vladimir B. Taranov, Gennady El
A 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 Sele’s modes. The wall modes with the disturbance of the interface being localised at the sidewalls of the cell dominate the dynamics of instability. Sele’s 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 MATHEMATICAL PHYSICS

Volume

171

Issue

2

Pages

675 - 682 (8)

Citation

PAVLOV, M.V., TARANOV, V.B. and EL, G.A., 2012. Generalized hydrodynamic reductions of the kinetic equation for a soliton gas. Theoretical and Mathematical Physics, 171 (2), pp.675-682.

Publisher

© Springer

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/ by/4.0/

Publication date

2012

Notes

The final publication is available at Springer via http://dx.doi.org/10.1007/s11232-012-0064-z

ISSN

0040-5779

Language

en

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