  We constrain the velocity power spectrum shape parameter $\Gamma$ in linear
theory using the nine bulk-flow and shear moments estimated from four recent
peculiar velocity surveys. For each survey, a likelihood function for $\Gamma$
was found after marginalizing over the power spectrum amplitude
$\sigma_8\Omega_m^{0.6}$ using constraints obtained from comparisons between
redshift surveys and peculiar velocity data. In order to maximize the accuracy
of our analyses, the velocity noise $\sigma_*$ was estimated directly for each
survey. A statistical analysis of the differences between the values of the
moments estimated from different surveys showed consistency with theoretical
predictions, suggesting that all the surveys investigated reflect the same
large scale flows. The peculiar velocity surveys were combined into a composite
survey yielding the constraint $\Gamma=0.13^{+0.09}_{-0.05}$. This value is
lower than, but consistent with, values obtained using redshift surveys and CMB
data.
