  The mechanisms that maintain turbulence in the interstellar medium (ISM) are
still not identified. This work investigates how we can distinguish between two
fundamental driving mechanisms: the accumulated effect of stellar feedback
versus the energy injection from Galactic scales. We perform a series of
numerical simulations describing a stratified star forming ISM subject to
self-consistent stellar feedback. Large scale external turbulent driving of
various intensities is added to mimic galactic driving mechanisms. We analyse
the resulting column density maps with a technique called Multi-scale
non-Gaussian segmentation that separates the coherent structures and the
Gaussian background. This effectively discriminates between the various
simulations and is a promising method to understand the ISM structure. In
particular the power spectrum of the coherent structures flattens above 60 pc
when turbulence is driven only by stellar feedback. When large-scale driving is
applied, the turn-over shifts to larger scales. A systematic comparison with
the Large Magellanic Cloud (LMC) is then performed. Only 1 out of 25 regions
has a coherent power spectrum which is consistent with the feedback-only
simulation. A detailed study of the turn-over scale leads us to conclude that
regular stellar feedback is not enough to explain the observed ISM structure on
scales larger than 60 pc. Extreme feedback in the form of supergiant shells
likely plays an important role but cannot explain all the regions of the LMC.
If we assume ISM structure is generated by turbulence, another large scale
driving mechanism is needed to explain the entirety of the observations.
