David Acheson


Instability of Vortex Leapfrogging

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.

(To run the software on a modern PC, I suggest using qb64 and consulting the notes here.)

Classical Dynamics and Control

An upside-down pendulum theorem

Not quite the Indian Rope Trick

Nonlinear inverted pendulum dynamics

Fluid Dynamics


'Valve'-effect at a critical layer

Enhanced spin-up

'Stability' as a catalyst for instability

Geophysical Fluid Dynamics

Magnetic instabilities of rotating fluids

Westward drift of the Earth's magnetic field

Astrophysical Fluid Dynamics

Magnetorotational instability

Magnetic buoyancy in the Sun

'Local' analysis of astrophysical instabilities

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