  We present a numerical study of the relation between the cosmic peculiar
velocity field and the gravitational acceleration field. We show that on mildly
non-linear scales (4-10 Mpc Gaussian smoothing), the distribution of the
Cartesian coordinates of each of these fields is well approximated by a
Gaussian. In particular, their kurtoses and negentropies are small compared to
those of the velocity divergence and density fields. We find that at these
scales the relation between the velocity and gravity field follows linear
theory to good accuracy. Specifically, the systematic errors in
velocity-velocity comparisons due to assuming the linear model do not exceed 6%
in beta. To correct for them, we test various nonlinear estimators of velocity
from density. We show that a slight modification of the alpha-formula proposed
by Kudlicki et al. yields an estimator which is essentially unbiased and has a
small variance.
