The self-induced motion of a helical vortex

Helical vortices have been studied for more than a century to understand basic aspects of fluid motion. Helical vortices appear both in nature, e.g. as tornadoes, and in many industrial applications associated with mixing and in wakes behind rotors. Owing to the complexity of the equations governing the self-induced motion of helical vortices, it has up to now not been possible to obtain closed-form solutions describing all aspects of the motion. An important issue concerns the difference between the self-induced motion of the helical structure and the movement of fluid particles located on the helix. Here, we revisit the equations governing both the motion of the helical vortex structure and the motion of material fluid elements on the axis of the helix, and for both cases derive closed-form solutions for the resulting velocities. As a part of the paper, we also devise potential applications of the achieved knowledge.