Arriving at the end of this review, we cannot escape the conclusion that the solution to the supergranulation puzzle is not as yet conspicuous. However, the combination of observational and numerical results indicates that a likely key to solve the problem is to understand the large-scale interactions between magnetic fields and velocity fields in the quiet Sun. In order to stimulate future work and discussions, we would like to conclude this work by dwelling on the suggestion that supergranulation is a feature of statistically steady saturated turbulent MHD convection in an extended domain.

We start with a few contextual comments that motivate this suggestion (Section 8.1) and then explore the main features and critical points of such a scenario (Section 8.2). We finally propose a set of numerical and observational studies whose results would significantly help make progress on the understanding of large-scale MHD turbulence in the quiet Sun (Section 8.3).

8.1 Preliminary comments

8.1.1 The large-scale tail of the kinetic power spectrum

8.1.2 Supergranulation, network and internetwork fields

8.2 Nonlinear MHD at large scales

8.2.1 Comparing energy spectra

8.2.2 Breaking the large-scale similarity of solar surface flows

8.2.3 Dynamical magnetic feedback: a tricky question

8.2.4 Comments on the equipartition argument

8.3 Suggestions for future research

8.1.1 The large-scale tail of the kinetic power spectrum

8.1.2 Supergranulation, network and internetwork fields

8.2 Nonlinear MHD at large scales

8.2.1 Comparing energy spectra

8.2.2 Breaking the large-scale similarity of solar surface flows

8.2.3 Dynamical magnetic feedback: a tricky question

8.2.4 Comments on the equipartition argument

8.3 Suggestions for future research

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