Forced hydromagnetic oscillations of a rapidly rotating fluid

A theoretical study is presented of the hydromagnetic waves which are generated in a rotating fluid when its boundaries are started into transverse oscillation. Particular attention is focused on the very low-frequency waves that occur when the rotation speed greatly exceeds the Alfvén speed, in view of their probable importance in connection with the dynamics of the Earth’s liquid core. Estimates of their magnetic field amplitude are obtained for the case when the viscosity of the fluid is very small, and it is found that the amplitude increases with the conductivity σs of the boundaries unless this exceeds a certain threshold value, in which case the amplitude is virtually independent of σs. When the motion of the boundaries is transient and of very high frequency, the magnetic field amplitude of the fluid oscillations at the forcing frequency may greatly exceed that of the accompanying low-speed hydromagnetic waves. The transient response is nevertheless of very limited spatial extent, and application of these results to the dynamics of the Earth’s deep interior then indicates that high-frequency magnetic fluctuations in the core (which are shielded from observation at the Earth’s surface by the skin effect in the mantle) cannot have sufficient amplitude to significantly enhance electromagnetic core-mantle coupling.