This research gives a new twist to a 100-year old problem in the theory of vortex motion.
A E H Love (1863-1940)
In 1894, Love showed that two identical vortex pairs can engage in a perpetual leapfrogging motion, but it now turns out that this motion can be unstable, in a very curious way.
"Walkabout" instability of vortex leapfrogging
The research is described in European Journal of Physics Vol. 21, pp 269-273 (2000), and the animation software leapfrog.zip has been specially written to accompany that paper.
Download and unzip, or, alternatively click on the individual, ready-to-run programs
contains pre-set animations of vortex leapfrogging
LEAP2.EXE shows the corresponding vortex trajectories
LEAP3.EXE allows the user to try different parameter values
Not quite the Indian Rope Trick
Nonlinear inverted pendulum dynamics
'Valve'-effect at a critical layer
'Stability' as a catalyst for instability
Magnetic instabilities of rotating fluids
Westward drift of the Earth's magnetic field
Magnetically-aided instability of differential rotation
Magnetic buoyancy in the Sun
'Local' analysis of astrophysical instabilities