  We investigate impacts of massive neutrinos on the cosmic velocity fields,
employing high-resolution cosmological $N$-body simulations provided by the
information-optimized CUBE code, where cosmic neutrinos are evolved using
collisionless hydrodynamics and their perturbations can be accurately resolved.
In this study we focus, for the first time, on the analysis of massive-neutrino
induced suppression effects in various cosmic velocity field components of
velocity magnitude, divergence, vorticity and dispersion. By varying the
neutrino mass sum $M_\nu$ from 0 -- 0.4 eV, the simulations show that, the
power spectra of vorticity -- exclusively sourced by non-linear structure
formation that is affected by massive neutrinos significantly -- is very
sensitive to the mass sum, which potentially provide novel signatures in
detecting massive neutrinos. Furthermore, using the chi-square statistic, we
quantitatively test the sensitivity of the density and velocity power spectra
to the neutrino mass sum. Indeed, we find that, the vorticity spectrum has the
highest sensitivity, and the null hypothesis of massless neutrinos is
incompatible with both vorticity and divergence spectra from $M_\nu=0.1$ eV at
high significance ($p$-value $= 0.03$ and $0.07$, respectively). These results
demonstrate clearly the importance of peculiar velocity field measurements, in
particular of vorticity and divergence components, in determination of neutrino
mass and mass hierarchy.
