Normal fluids like water and air are described by the famous Navier-Stokes Equations, which apply to any system that respects Galileo symmetry. However, when the symmetry group is more exotic, novel terms may modify the NS equations and lead to interesting behaviour. For Farrell, Huang, Lucas (2022), we investigated a fluid with the symmetry of a helix: only the combination $\ P_z + L_z/\xi\ $ is a conserved quantity, not $\ P_z$ or $\ L_z \ $ separately. Interestingly, the transport coefficients of the helical theory are partially fixed by symmetry alone, and the fluid also features transverse responses, for example supplying a torque in the presence of a uniform electric field!

The figure is a cartoon illustrating helical symmetry.