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Lookup NU author(s): Matthew Buckley, Professor Paul BushbyORCiD
Localized states are found in many pattern forming systems. The aim of this paper is to investigate the occurrence of oscillatory localized states in two-dimensional Boussinesq magnetoconvection. Initially considering an idealized model, in which the vertical structure of the system has been simplified by a projection onto a small number of Fourier modes, we find that these states are restricted to the low zeta regime (where zeta represents the ratio of the magnetic to thermal diffusivities). These states always exhibit bistability with another nontrivial solution branch; in other words, they show no evidence of subcritical behavior. This is due to the weak flux expulsion that is exhibited by these time-dependent solutions. Using the results of this parameter survey, we locate corresponding states in a fully resolved two-dimensional system, although the mode of oscillation is more complex in this case. This is the first time that a localized oscillatory state, of this kind, has been found in a fully resolved magnetoconvection simulation. DOI: 10.1103/PhysRevE.87.023019
Author(s): Buckley MC; Bushby PJ
Publication type: Article
Publication status: Published
Journal: Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
Year: 2013
Volume: 87
Issue: 2
Print publication date: 25/02/2013
ISSN (print): 1539-3755
ISSN (electronic): 1550-2376
Publisher: American Physical Society
URL: http://dx.doi.org/10.1103/PhysRevE.87.023019
DOI: 10.1103/PhysRevE.87.023019
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