Localised solutions in Magnetoconvection
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.