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The fragmentation of gas to form stars in molecular clouds is intrinsicallylinked to the turbulence within them. These internal motions are set at thebirth of the cloud and may vary with galactic environment and as the cloudevolves. In this paper, we introduce a new suite of 15 high-resolutionmolecular cloud simulations using the moving mesh code AREPO, to investigatethe role of different decaying turbulent modes (mixed, compressive andsolenoidal) 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 theinitial turbulent mode, whereas the initial gravitational potential dominatesdense regions. Solenoidal seeded models thus give rise to a diffuse cloud withfilament-like morphology, and an excess of brown dwarf mass fragments.Compressive seeded models have an early onset of star-formation, cluster-likemorphologies and a higher accretion rate, along with overbound clouds, comparedto other simulations. Filaments identified using DisPerSE, and analyzed througha new Python toolkit we develop and make publicly available with this workcalled FIESTA, show no clear trend in lengths, masses and densities betweeninitial turbulent modes. Overbound clouds, however, produce more filaments andthus have more mass in filaments. The hubs formed by converging filaments arefound to favour star-formation, with surprisingly similar mass distributionsindependent of the number of filaments connecting the hub.

Decaying turbulence in molecular clouds: how does it affect filament networks and star formation?