Numerical simulation of the interaction of two thin tubular vortices in an incompressible inviscid fluid. In the initial condition one vortex is a circular ring, the other is a toroidal helix that coils five times around the vortex ring (the radius of the coils being 0.15R, where R is the radius of the circular ring). The two vortices have the same circulation and cross-sectional radius (0.03R), and are represented by 600 nodes. The velocity field is computed using the Rosenhead-Moore approximation to the Biot-Savart law, the nodes and passive tracers are moved using a fourth-order Runge-Kutta method with fixed time step. As the vortices translate along and rotate around the symmetry axis they change shape almost periodically: at regular intervals the helico-toroidal vortex becomes an almost circular vortex ring and vice versa. The video shows five 'periods' of this evolution from three different viewpoints.
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