David Acheson



Research






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


Over-reflection

'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





Back to Home Page