  We investigate how rotationally-constrained, deep convection might give rise
to supergranulation, the largest distinct spatial scale of convection observed
in the solar photosphere. While supergranulation is only weakly influenced by
rotation, larger spatial scales of convection sample the deep convection zone
and are presumably rotationally influenced. We present numerical results from a
series of nonlinear, 3-D simulations of rotating convection and examine the
velocity power distribution realized under a range of Rossby numbers. When
rotation is present, the convective power distribution possesses a pronounced
peak, at characteristic wavenumber $\ell_\mathrm{peak}$, whose value increases
as the Rossby number is decreased. This distribution of power contrasts with
that realized in non-rotating convection, where power increases monotonically
from high to low wavenumbers. We find that spatial scales smaller than
$\ell_\mathrm{peak}$ behave in analogy to non-rotating convection. Spatial
scales larger than $\ell_\mathrm{peak}$ are rotationally-constrained and
possess substantially reduced power relative to the non-rotating system. We
argue that the supergranular scale emerges due to a suppression of power on
spatial scales larger than $\ell\approx100$ owing to the presence of deep,
rotationally-constrained convection. Supergranulation thus represents the
largest non-rotationally-constrained mode of solar convection. We conclude that
the characteristic spatial scale of supergranulation bounds that of the deep
convective motions from above, making supergranulation an indirect measure of
the deep-seated dynamics at work in the solar dynamo. Using the spatial scale
of supergranulation in conjunction with our numerical results, we estimate an
upper bound of 10 m s$^{-1}$ for the Sun's bulk rms convective velocity.
