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The kinematic analysis of dark matter and hydrodynamical simulations suggeststhat the vorticity in large-scale structure is mostly confined to, andpredominantly aligned with their filaments, with an excess of probability of 20per cent to have the angle between vorticity and filaments direction lower than60 degrees relative to random orientations. The cross sections of thesefilaments are typically partitioned into four quadrants with opposite vorticitysign, arising from multiple flows, originating from neighbouring walls. Thespins of halos embedded within these filaments are consistently aligned withthis vorticity for any halo mass, with a stronger alignment for the mostmassive structures up to an excess of probability of 165 per cent. On largescales, adiabatic/cooling hydrodynamical simulations display the same vorticityin the gas as in the dark matter. The global geometry of the flow within thecosmic web is therefore qualitatively consistent with a spin acquisition forsmaller halos induced by this large-scale coherence, as argued in Codis et al.(2012). In effect, secondary anisotropic infall (originating from thevortex-rich filament within which these lower-mass halos form) dominates theangular momentum budget of these halos. The transition mass from alignment toorthogonality is related to the size of a given multi-flow region with a givenpolarity. This transition may be reconciled with the standard tidal torquetheory if the latter is augmented so as to account for the larger scaleanisotropic environment of walls and filaments.

Swirling around filaments: are large-scale structure vortices spinning up dark halos?