  We study the generation of vorticity and velocity dispersion by orbit
crossing using cosmological numerical simulations, and calculate the
backreaction of these effects on the evolution of large-scale density and
velocity divergence power spectra. We use Delaunay tessellations to define the
velocity field, showing that the power spectra of velocity divergence and
vorticity measured in this way are unbiased and have better noise properties
than for standard interpolation methods that deal with mass weighted
velocities. We show that high resolution simulations are required to recover
the correct large-scale vorticity power spectrum, while poor resolution can
spuriously amplify its amplitude by more than one order of magnitude. We
measure the scalar and vector modes of the stress tensor induced by orbit
crossing using an adaptive technique, showing that its vector modes lead, when
input into the vorticity evolution equation, to the same vorticity power
spectrum obtained from the Delaunay method. We incorporate orbit crossing
corrections to the evolution of large scale density and velocity fields in
perturbation theory by using the measured stress tensor modes. We find that at
large scales (k~0.1 h/Mpc) vector modes have very little effect in the density
power spectrum, while scalar modes (velocity dispersion) can induce percent
level corrections at z=0, particularly in the velocity divergence power
spectrum. In addition, we show that the velocity power spectrum is smaller than
predicted by linear theory until well into the nonlinear regime, with little
contribution from virial velocities.
