  Clustering of a perfect fluid does not lead to the generation of vorticity.
It is the collisionless nature of dark matter, inducing velocity dispersion and
shell crossing, which is at the origin of cosmological vorticity generation. In
this paper we investigate the generation of vorticity during the formation of
cosmological large scale structure using the public relativistic N-body code
$\textit{gevolution}$. We test several methods to compute the vorticity power
spectrum and we study its convergence with respect to the mass and grid
resolution of our simulations. We determine the power spectrum, the spectral
index on large-scales, the amplitude of the peak position and their time
evolution. We also compare the vorticity extracted from our simulations with
the vector perturbations of the metric. Our results are accompanied by
resolution studies and compared with previous studies in the literature.
