A set of equal, coaxial helical vortices approximates the tip vortices in the wake of multi-bladed wind turbines, propellers or rotors. This video shows the advection of fluid particles by two helical vortices in an inviscid, incompressible, and unbounded fluid. The first simulation shows regular advection by steadily moving vortices of small pitch and relatively large core (helix pitch: L=pi, helix radius: R=1, vortex core radius: a=0.1). The second simulation shows chaotic advection by leapfrogging vortices; these are the same as before except that, in the initial condition, one vortex was shifted a small distance, L/40, along the helices' axis. The evolution is computed by integrating the Rosenhead-Moore approximation to the Biot-Savart law with a fourth-order Runge-Kutta scheme. In the initial condition, passive tracers are randomly distributed within a coaxial cylinder of radius 1.5R and length L/4. The video shows the tracers only when they find themselves within a thin layer around the meridional plane perpendicular to the sightline.
This work is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License. Any reuse must credit the author(s) and provide a link back to this page.