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Title: Generalized hydrodynamic reductions of the kinetic equation for a soliton gas
Authors: Pavlov, Maxim V.
Taranov, Vladimir B.
El, G.A.
Keywords: Kinetic equation
Riemann invariant
Hydrodynamic reduction
Issue Date: 2012
Publisher: © Springer
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.
Abstract: 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.
Description: The final publication is available at Springer via http://dx.doi.org/10.1007/s11232-012-0064-z
Version: Accepted for publication
DOI: 10.1007/s11232-012-0064-z
URI: https://dspace.lboro.ac.uk/2134/16943
Publisher Link: http://dx.doi.org/10.1007/s11232-012-0064-z
ISSN: 0040-5779
Appears in Collections:Published Articles (Maths)

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