  Discovering the mass of neutrinos is a principle goal in high energy physics
and cosmology. In addition to cosmological measurements based on two-point
statistics, the neutrino mass can also be estimated by observations of neutrino
wakes resulting from the relative motion between dark matter and neutrinos.
Such a detection relies on an accurate reconstruction of the dark
matter-neutrino relative velocity which is affected by non-linear structure
growth and galaxy bias. We investigate our ability to reconstruct this relative
velocity using large N-body simulations where we evolve neutrinos as distinct
particles alongside the dark matter. We find that the dark matter velocity
power spectrum is overpredicted by linear theory whereas the neutrino velocity
power spectrum is underpredicted. The magnitude of the relative velocity
observed in the simulations is found to be lower than what is predicted in
linear theory. Since neither the dark matter nor the neutrino velocity fields
are directly observable from galaxy or 21 cm surveys, we test the accuracy of a
reconstruction algorithm based on halo density fields and linear theory.
Assuming prior knowledge of the halo bias, we find that the reconstructed
relative velocities are highly correlated with the simulated ones with
correlation coefficients of 0.94, 0.93, 0.91 and 0.88 for neutrinos of mass
0.05, 0.1, 0.2 and 0.4 eV. We confirm that the relative velocity field
reconstructed from large scale structure observations such as galaxy or 21 cm
surveys can be accurate in direction and, with appropriate scaling, magnitude.
