  The solar photosphere provides us with a laboratory for understanding
turbulence in a layer where the fundamental processes of transport vary rapidly
and a strongly superadiabatic region lies very closely to a subadiabatic layer.
Our tools for probing the turbulence are high-resolution spectropolarimetric
observations such as have recently been obtained with the two sunrise missions,
and numerical simulations. Our aim is to study photospheric turbulence with the
help of Fourier power spectra that we compute from observations and
simulations. We also attempt to explain some properties of the photospheric
overshooting flow with the help of its governing equations and simulations. We
find that quiet-Sun observations and smeared simulations exhibit a power-law
behavior in the subgranular range of their Doppler velocity power spectra with
an index of$~\approx -2$. The unsmeared simulations exhibit a power-law index
of$~\approx -2.25$. The smearing considerably reduces the extent of the
power-law-like portion of the spectra. Therefore, the limited spatial
resolution in some observations might eventually result in larger uncertainties
in the estimation of the power-law indices.
  The simulated vertical velocity power spectra as a function of height show a
rapid change in the power-law index from the solar surface to $300$~km above
it. A scale-dependent transport of the vertical momentum occurs. At smaller
scales, the vertical momentum is more efficiently transported sideways than at
larger scales. This results in less vertical velocity power transported upward
at small scales than at larger scales and produces a progressively steeper
vertical velocity power law below $180$ km. Above this height, the gravity work
progressively gains importance at all scales, making the atmosphere
progressively more hydrostatic and resulting in a gradually less steep power
law.
