Abstract:

Nobody knows when and who first discovered the directional property of the magnetic compass needle, but there is some evidence that it was known in China more than 4000 years ago. Early ``explanations" were wild; it was supposed, for example, that the compass needle was attracted by the pole star. Gauss succeeded in the 1830s in establishing however that the source of the Earth's magnetism lay within it, but the idea that the source was permanent magnetism was soon ruled out; the source had to be the magnetism associated with the flow of electric current, but what is the origin of the electric current? It was discovered in 1906 that the Earth has a dense central core, made largely of fluid, and it was soon agreed that this core is rich in iron, a good electrical conductor. In 1919, Larmor suggested that there is a fluid dynamo operating inside the core, which creates the electric currents that make the observed magnetic fields.

And so an attractive field of applied mathematics was born, a branch of the subject of magnetohydrodynamics, or MHD for short. This studies the mutual interaction of magnetic fields and moving, electrically-conducting fluids; the motion of the fluid in the presence of the magnetic field produces electric currents that create ``induced" fields, and the magnetic fields and electric currents react back to alter the motion of the fluid. In a fluid dynamo, the inducing field and induced field are supposed to be one and the same. But is this possible? Isn't it hoisting oneself up by one's own bootstraps? The early proofs that fluid dynamos can in principle exist was achieved through beautiful applications of asymptotic theory, but dynamical questions are nonlinear and have mostly to be answered by computation. Now several groups have simulated the Earth's dynamo and have created models that encouragingly resemble the observed Earth's magnetic field. Some of this work will be reviewed.