  Supergranulation is characterized by horizontally divergent flows with
typical length scales of 32 Mm in the solar photosphere. Unlike granulation,
the size of which is comparable to both the thickness of the radiative boundary
layer and local scale height of the plasma in the photosphere, supergranulation
does not reflect any obvious length scale of the solar convection zone. Early
suggestions that the depth of second helium ionization is important are not
supported by numerical simulations. Thus the origin of the solar
supergranulation remains largely a mystery. Moreover, observations of flows in
the photosphere using either Doppler imaging or correlation or feature tracking
show a monotonic decrease in power at scales larger than supergranulation. Both
local area and global spherical shell simulations of solar convection by
contrast show the opposite, a power law increase in horizontal flow amplitudes
to low wavenumber. Here we examine this disparity, and investigate how the
solar supergranulation may arise as a consequence of strong photospheric
driving and non-local heat transport by cool diving plumes. Using three
dimensional anelastic simulations with surface driving, we show that the
kinetic energy of largest convective scales in the upper layers of a stratified
domain reflects the depth of transition from strong buoyant driving to
adiabatic stratification below. We interpret the observed monotonic decrease in
solar convective power at scales larger than supergranulation to be a
consequence of this rapid transition, and show how the supergranular scale can
be understood as the largest buoyantly driven mode of convection in the Sun.

Solar and Stellar Astrophysics