  The peculiar velocity of a mass tracer is on average aligned with the dipole
modulation of the surrounding mass density field. We present a first
measurement of the correlation between radial peculiar velocities of objects in
the cosmicflows-3 catalog and the dipole moment of the 2MRS galaxy distribution
in concentric spherical shells centered on these objects. Limiting the analysis
to cosmicflows-3 objects with distances of $100 \rm Mpc h^{-1}$, the
correlation function is detected at a confidence level $> 4\sigma$. The
measurement is found consistent with the standard $\Lambda$CDM model at $<
1.7\sigma$ level. We formally derive the constraints
$0.32<\Omega^{0.55}\sigma_8<0.48$ ($68\% $ confidence level) or equivalently
$0.34<\Omega^{0.55}/b<0.52$, where $b$ is the galaxy bias factor. Deeper and
improved peculiar velocity catalogs will substantially reduce the
uncertainties, allowing tighter constraints from this type of correlations.
