  The fragmentation of gas to form stars in molecular clouds is intrinsically
linked to the turbulence within them. These internal motions are set at the
birth of the cloud and may vary with galactic environment and as the cloud
evolves. In this paper, we introduce a new suite of 15 high-resolution 3D
molecular cloud simulations using the moving mesh code AREPO to investigate the
role of different decaying turbulent modes (mixed, compressive and solenoidal)
and virial ratios on the evolution of a $10^4\mathrm{M}_{\odot}$ molecular
cloud. We find that diffuse regions maintain a strong relic of the initial
turbulent mode, whereas the initial gravitational potential dominates dense
regions. Solenoidal seeded models thus give rise to a diffuse cloud with
filament-like morphology, and an excess of brown dwarf mass fragments.
Compressive seeded models have an early onset of star-formation, centrally
condensed morphologies and a higher accretion rate, along with overbound
clouds. 3D filaments identified using DisPerSE and analyzed through a new
Python toolkit we develop and make publicly available with this work called
FIESTA, show no clear trend in lengths, masses and densities between initial
turbulent modes. Overbound clouds, however, produce more filaments and thus
have more mass in filaments. The hubs formed by converging filaments are found
to favour star-formation, with surprisingly similar mass distributions
independent of the number of filaments connecting the hub.
