Localised Oscillatory States in Magnetoconvection

TL;DR

This paper investigates oscillatory localised states in 2D magnetoconvection, revealing their occurrence in idealised models and fully-resolved simulations, and highlighting their bistability and weak flux expulsion characteristics.

Contribution

It is the first to identify localised oscillatory states in fully-resolved 2D magnetoconvection simulations, extending understanding from idealised models.

Findings

Oscillatory localised states occur in low ζ regimes.

States exhibit bistability with other solutions.

First observation of such states in fully-resolved simulations.

Abstract

Localised states are found in many pattern forming systems. The aim of this paper is to investigate the occurrence of oscillatory localised states in two-dimensional Boussinesq magnetoconvection. Initially considering an idealised 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 non-trivial solution branch, in other words they show no evidence of subcritical behaviour. 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 localised oscillatory state, of this kind, has been found in a fully-resolved magnetoconvection simulation.