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Aims: The interactions of velocity scales on the Sun's surface, fromgranulation to supergranulation are still not understood, nor are theirinteraction with magnetic fields. We thus aim at giving a better description ofdynamics in the mesoscale range which lies between the two scales mentionedabove. Method: We analyse a 48h high-resolution time sequence of the quiet Sunphotosphere at the disk center obtained with the Solar Optical Telescopeonboard Hinode. The observations, which have a field of view of 100\arcsec$\times$ 100 \arcsec, typically contain four supergranules. We monitorin detail the motion and evolution of granules as well as those of the radialmagnetic field. Results: This analysis allows us to better characterize Treesof Fragmenting Granules issued from repeated fragmentation of granules,especially their lifetime statistics. Using floating corks advected by measuredvelocity fields, we show their crucial role in the advection of the magneticfield and in the build up of the network. Finally, thanks to the long durationof the time series, we estimate that the turbulent diffusion coefficientinduced by horizontal motion is approximately $430 \mathrm{km}^2\mathrm{s}^{-1}$. Conclusions: These results demonstrate that the long livingfamilies contribute to the formation of the magnetic network and suggest thatsupergranulation could be an emergent length scale building up as smallmagnetic elements are advected and concentrated by TFG flows. Our estimate forthe magnetic diffusion associated with this horizontal motion might provide auseful input for mean-field dynamo models.

Mesoscale dynamics on the Sun's surface from HINODE observations