The energetic signature of supergranulation lies in the 10 – 100 Mm range of the horizontal kinetic energy spectrum of solar surface convection, i.e., in the large-scale tail of the spectrum extending beyond the injection range (see Figure 4 and Figure 22 in Nordlund et al., 2009 for instance). Both observationally and numerically derived kinetic energy spectra show us that there is some kinetic energy in that range, even though it lies beyond the typical injection scale12. But, in all hydrodynamic simulations of supergranulation-scale convection to date, the kinetic energy of the flow in that range has been observed to be a monotonically decreasing, quasi-self-similar function of the horizontal scale. In the solar photosphere, estimates for the associated typical horizontal velocities range from 1 – 2 km s–1 at granulation scale to 50 – 100 m s–1 at 100 Mm.
These results suggest two conclusions. First, horizontal flows are naturally generated at all scales in the 10 – 100 Mm range by an essentially hydrodynamic process. Second, supergranulation scales do not appear to be singled out by that process, to the best of today’s knowledge. Hence, even though we cannot yet rule out that a purely hydrodynamic process would make supergranulation a special scale, we should consider alternative scenarios. The suggestion that supergranulation could be a large-scale dynamical feature of MHD turbulence in the quiet photosphere is particularly appealing in this respect. It is notably supported by recent observations of the disappearance of the spectral bump of supergranulation during the emergence of a pore (Rieutord et al., 2010).
Supergranulation and the magnetic network are strongly correlated observationally (see Simon and Leighton, 1964, and Section 4.6). The process of magnetic network formation has often been described in simple kinematic terms by assuming that small-scale magnetic fields are locally intensified and stochastically advected to larger scales, being eventually concentrated at the boundaries of a preexisting supergranulation flow field. Here, we would like to take on a somewhat more dynamical and less causal point of view, by simply suggesting that the magnetic network and supergranulation may originate in a coupled, undistinguishable dynamical way. This suggestion notably echoes the conclusions of Crouch et al. (2007), who describe supergranulation as an “emergent length scale” based on the results of numerical n-body toy models mimicking MHD effects.
Also, even though internetwork and network fields have been historically separated into two families based on their different strength, distribution, and orientation properties, there is no a priori reason to believe that their dynamics are physically disconnected, so we wish to keep both types of fields in the following discussion of the dynamics at large scales (see also Section 4.6.2 and the findings of Meunier et al., 2007a regarding the correlation between internetwork field strengths and supergranulation scales). From an MHD turbulence perspective, they can all be considered as part of a continuous hierarchy of magnetic structures whose energy distribution and geometrical properties vary with scale in some yet to be understood way (for a similar argument, see Stenflo and Holzreuter, 2003a). Note that this statement is not quite as extreme as saying that the structure of the magnetic field is self-similar (Section 4.6.3).
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