How do velocity structure functions trace gas dynamics in simulated
  molecular clouds?
  Context. Supersonic disordered flows accompany the formation and evolution of
MCs. It has been argued that turbulence can support against gravitational
collapse and form hierarchical sub-structures. Aims. We study the time
evolution of simulated MCs to investigate: What physical process dominates the
driving of turbulent flows? How can these flows be characterised? Do the
simulated flows agree with observations? Methods. We analyse three MCs that
have formed self-consistently within kpc-scale numerical simulations of the
ISM. The simulated ISM evolves under the influence of physical processes
including self-gravity, stratification, magnetic fields, supernova-driven
turbulence, and radiative heating and cooling. We characterise the flows using
VSFs with/out density weighting or a density cutoff, and computed in one or
three dimensions. Results. In regions with sufficient resolution, the
density-weighted VSFs initially appear to follow the expectations for uniform
turbulence consistent with Larson's size-velocity relationship. SN blast wave
impacts produce short-lived coherent motions at large scales, increasing the
scaling exponents for a crossing time. Gravitational contraction drives
small-scale motions, producing scaling coefficients that drop or even turn
negative as small scales become dominant. Conclusions. We conclude that two
different effects coincidentally reproduce Larson's size velocity relationship.
Initially, uniform turbulence dominates, so the energy cascade produces VSFs
consistent with Larson's relationship. Later, contraction dominates, the
density-weighted VSFs become much shallower or even inverted, but the
relationship of the global average velocity dispersion of the MCs to their
radius follows Larson's relationship, reflecting virial equilibrium or
free-fall collapse. The injection of energy by shocks is visible in the VSFs,
but decays within a crossing time.
