  The turbulent dynamics of nearby and extragalactic gas structures can be
studied with the column density power spectrum, which is often described by a
broken power-law.In an extragalactic context, the breaks in the power spectra
have been interpreted to constrain the disc scale height, which marks a
transition from 2D disc-like to 3D motion. However, this interpretation has
recently been questioned when accounting for instrumental effects. We use
numerical simulations to study the spatial power spectra of isolated galaxies
and investigate the origins of the break scale. We split the gas into various
phases and analyze the time evolution of the power spectrum characteristics,
such as the slope(s) and the break scale. We find that the break scale is phase
dependent. The physics traced by the break scale also differ: in the warm gas
it marks the transition from 2D (disk-like) to 3D (isotropic) turbulence. In
the cold gas, the break scale traces the typical size of molecular clouds. We
further show that the break scale almost never traces the disc scale height. We
study turbulent properties of the ISM to show that, in the case where the break
scale traces a transition to isotropic turbulence, the fraction of required
accretion energy to sustain turbulent motions in the ISM increases
significantly. Lastly, we demonstrate through simulated observations that it is
crucial to account for observational effects, such as the beam and instrumental
noise, in order to accurately recover the break scale in real observations.
