Localised
solutions in Magnetoconvection
Steve Houghton
DAMTP, CMS, University of Cambridge
Localised solutions have been observed in two--dimensional
numerical simulations of thermal convection in the presence of an imposed
magnetic field. These solutions have
just one convection roll while the remainder of the fluid is static. A simple model is considered to help
understand the formation of this type of solution. This model is compared to others that may be derived on symmetry
grounds, forming a coupled cell system, or by performing a boundary layer
analysis. Preliminary numerical results
in three--dimensions also show localised structures. Solutions of this type may be related to the bright umbral dots
that are observed within the dark, central umbra of sunspots.