  We present the hydrodynamics of fluids in three spatial dimensions with
helical symmetry, wherein only a linear combination of a rotation and
translation is conserved in one of the three directions. The hydrodynamic
degrees of freedom consist of scalar densities (e.g. energy or charge) along
with two velocity fields transverse to the helical axis when the corresponding
momenta are conserved. Nondissipative hydrodynamic coefficients reminiscent of
chiral vortical coefficients arise. We write down microscopic Hamiltonian
dynamical systems exhibiting helical symmetry, and we demonstrate using kinetic
theory that these systems will generically exhibit the new helical phenomena
that we predicted within hydrodynamics. We also confirm our findings using
modern effective field theory techniques for hydrodynamics. We postulate
regimes where pinned cholesteric liquid crystals may possess transport
coefficients of a helical fluid, which appear to have been overlooked in
previous literature.
