  Turbulent properties of the quiet Sun represent the basic state of surface
conditions, and a background for various processes of solar activity. Therefore
understanding of properties and dynamics of this `basic' state is important for
investigation of more complex phenomena, formation and development of observed
phenomena in the photosphere and atmosphere. For characterization of the
turbulent properties we compare kinetic energy spectra on granular and
sub-granular scales obtained from infrared TiO observations with the New Solar
Telescope (Big Bear Solar Observatory) and from 3D radiative MHD numerical
simulations ('SolarBox' code). We find that the numerical simulations require a
high spatial resolution with 10 - 25 km grid-step in order to reproduce the
inertial (Kolmogorov) turbulence range. The observational data require an
averaging procedure to remove noise and potential instrumental artifacts. The
resulting kinetic energy spectra show a good agreement between the simulations
and observations, opening new perspectives for detailed joint analysis of more
complex turbulent phenomena on the Sun, and possibly on other stars. In
addition, using the simulations and observations we investigate effects of
background magnetic field, which is concentrated in self-organized complicated
structures in intergranular lanes, and find an increase of the small-scale
turbulence energy and its decrease at larger scales due to magnetic field
effects.
