  We investigate the effects of intrinsic alignments (IA) of dark-matter halo
shapes on cosmic density and velocity fields from cluster to cosmic scales
beyond 100 Mpc/h. Besides the density correlation function binned by the halo
orientation angle which was used in the literature, we introduce, for the first
time, the corresponding two velocity statistics, the angle-binned pairwise
infall momentum and momentum correlation function. Using large-volume,
high-resolution N-body simulations, we measure the alignment statistics of
density and velocity, both in real and redshift space. We find that the
alignment signal is not amplified by redshift-space distortions at linear
scales. Behaviors of IA in the velocity statistics are similar to those in the
density statistics, except that the halo orientations are aligned with the
velocity field up to a scale larger than those with the density field, x>100
Mpc/h. On halo scales, x~ R_{200m} ~ 1 Mpc/h, we detect a sharp steepening in
the momentum correlation associated with the physical halo boundary, or the
splashback feature, which is found more prominent than in the density
correlation. Our results indicate that observations of IA with the velocity
field can provide additional information on cosmological models from large
scales and on physical sizes of halos from small scales.
