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.