Abstract
The fine structure present in sunspot penumbrae first appears when filamentary convection sets in at the outer edge of large pores, coinciding with an increase in magnetic field inclination to the vertical. The formation of this filamentary structure is investigated in a highly idealized Boussinesq model. A two-dimensional equilibrium is constructed with the magnetic field at the bottom of the layer concentrated towards one side of the box, but fanning out towards the top of the layer, mimicking a sunspot. This two-dimensional steady state is then perturbed in the third direction, to seek filamentary instabilities leading to a filamentary structure. The two-dimensional model is found to be highly unstable for a range of transverse wavenumbers. The form of the instability is such that an alternating pattern of bright and dark filaments develops at the upper surface. This is the first numerical evidence of filamentary instabilities driven by external convection.
Published Version
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