On the patterns of the solar granulation and supergranulation

We study the cellular patterns of the white light granulation and of the chromospheric Ca II K supergranular network. We apply a gradient-based tessellation algorithm to define the cell outlines. The geometry of the patterns formed by the associated granular and supergranular flows are very similar, in spite of the substantial difference in length scale. We compare these patterns to generalized Voronoi foams and conclude that both convective patterns are very nearly compatible with an essentially random distribution of upflow centers, with the downflow boundaries determined by the competing strengths of outflows of neighboring upwellings. There appears to be a slight clustering in upflow positions for the granulation, consistent with the granular evolution. This slight preference for large granules to be surrounded by somewhat smaller ones makes the granular and supergranular patterns differ enough to allow a correct identification in three out of four cases by eye. The model analogy suggests that the range in outflow strengths is remarkably small. The patterns appear to be rather insensitive to the details of the competing forces that establish the pattern of the downflow network: similar patterns result under very different conditions, so that little can be learned about the details of the forces involved by studying the geometry of these patterns only.