List of Figures

View Image Figure 1:
Left: the entropy profile as a function of depth, as estimated by numerical simulations or crude mean-field models like the mixing length theory. Right: section of a cool plume diving from the surface. As it penetrates into the isentropic background, the plume increases both its mass and momentum flux by turbulent mass entrainment (represented by curly arrows). Its horizontal scale grows proportionally to depth, the aperture angle of the cone being around 0.1. At a given depth, the typical size of energetic eddies is like the width of the plume while a mean flow at the scale of the depth is also generated. From this model, we see that the length scale characterising the buoyant flow at a given depth increases monotonically with depth (image by Mark Rast, see External Link and Clyne et al., 2007).
View Image Figure 2:
A Dopplergram revealing the supergranulation pattern (credits SOHO/MDI/ESA).
View Image Figure 3:
The supergranulation horizontal velocity field as obtained by granule tracking (from Rieutord et al., 2008).
View Image Figure 4:
Kinetic energy spectra of solar surface flows. (a) The power spectrum of the line-of-sight velocity using SOHO/MDI Doppler data (Hathaway et al., 2000). The supergranulation peak near ℓ = 120 is clearly visible, while the granulation peak expected around ℓ = 3000 is eroded and effectively shifted to larger scales (ℓ ∼ 1500) due to time-averaging. (b) From the CALAS camera at Pic du Midi. Power spectrum (in relative units) of the horizontal velocity obtained from granule tracking for different time averages (Rieutord et al., 2008). (c) Absolute spectral density in km3 s–2 also derived from granule tracking, but applied to Hinode/SOT data (Rieutord et al., 2010). In (b) and (c) the power spectra are those defined in Equation (1View Equation).
View Image Figure 5:
(a) Correlation between the horizontal divergence and vertical vorticity of the supergranulation flow as a function of latitude (from Gizon and Duvall Jr, 2003). (b) Schematic view of anticyclones at the surface of the rotating Sun.
View Image Figure 6:
A view of the chromospheric network at the Ca+K3 line at 393.37 nm (from Meudon Observatory).
View Image Figure 7:
Magnetic field distribution (grey scale levels) on the supergranulation boundaries. The black dots show the final positions of floating corks that have been advected by the velocity field computed from the average motion of granules. The distribution of corks very neatly matches that of the magnetic field. (from Roudier et al., 2009).
View Image Figure 8:
Structure of flows surrounding a sunspot, as inferred from helioseismology (from Hindman et al., 2009).
View Image Figure 9:
The rotating MHD Rayleigh–Bénard convection problem.
View Image Figure 10:
Snapshots of temperature fluctuations in a vertical plane, from numerical simulations of Rayleigh–Bénard convection in a slender cylindrical cell at Pr = 0.7 and Rayleigh-numbers (a) 2 × 107, (b) 2 × 109, and (c) 2 × 1011 (from Verzicco and Camussi, 2003).
View Image Figure 11:
Radial velocity snapshots at various depths in global simulations of convection in shallow spherical shells, down to supergranulation scales (from DeRosa et al., 2002).
View Image Figure 12:
Comparison between horizontal temperature maps in an idealised simulation of large-scale compressible convection in a stratified polytropic atmosphere (left, aspect ratio 42, see Rincon et al., 2005 for details) and horizontal temperature maps in a realistic simulation of large-scale solar-like convection (right, aspect ratio 10, see Rieutord et al., 2002 for details). Top: z = 0.99d (left) and at optical depth τ = 1 (right), respectively (surface). Middle: half-depth of the numerical domain. Bottom: bottom of the numerical domain. The emergence of the granulation pattern in the surface layers is clearly visible in both types of simulations, on top of a larger-scale mesoscale dynamics extending down to deeper layers.
View Image Figure 13:
Horizontal maps of (a) temperature and (b) vertical magnetic field fluctuations in the surface layers of local realistic simulations of large-scale MHD convection (from Ustyugov, 2009).
View Image Figure 14:
A schematic view of the supergranulation phenomenon, as constrained by observations. λ is the scale where the horizontal kinetic energy spectral density is maximum. d is the diameter of “coherent structures” (supergranules). The red and blue patches depict the warm and cold regions of the flow. I.N.B denotes the internetwork magnetic field. Note that the indicated internetwork and network fields geometries roughly correspond to the standard historical picture of quiet Sun magnetic fields and their relation to supergranulation (Section 4.6). As discussed in Sections 4.6.2 and 8, this picture must be significantly nuanced in reality, as the dichotomy between network and internetwork fields is probably not quite as clear as indicated in this drawing.
View Image Figure 15:
A tentative log-log spectral-space description of nonlinear MHD turbulence in the quiet photosphere. The kinetic energy spectrum is represented by a full red line and the magnetic energy spectrum by a dashed blue line (k = 2π∕L). The thin dotted red line is representative of the results of state-of-the-art hydrodynamic simulations of supergranulation-scale convection (Stein et al., 2009a). The ordering of the small-scale cutoffs results from Pm ≪ 1 (see Section 2.2). A rather flat spectral slope for the magnetic spectrum has been represented in the range of scales smaller than 10 Mm in accordance with the data of Lee et al. (1997); Abramenko et al. (2001), and Harvey et al. (2007). The shape of the small-scale part of the spectrum below 0.5 – 1 Mm and of the large-scale part of the spectrum beyond 10 Mm are very speculative (Section 4.6.3), as we do not know what kind of MHD processes are at work in these ranges of scales. As indicated in the text, the field geometry and most energetic scales at subgranulation scales are still controversial issues (e.g., López Ariste et al., 2010) and the field production mechanism itself is a matter of debate (Vögler and Schüssler, 2007). Finally, the relative amplitude of the magnetic and kinetic energy spectra is somewhat arbitrary but has been calibrated so as to comply with the argument developed in the text.