By Tsuneji Rikitake
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Extra info for Electromagnetism and the Earth's Interior
D . wave in a fluid of density ρ, propagating along magnetic 1 / 2 1 / 2 -1 lines of force in a magnetic field of intensity H9 travels a distance α in a period 4 π ρ α # which is comparable with the periods obtained above. 3ρ αΗ~ . Although we have been dealing only with M . H . D . D. 27. Magnetic lines of force for the lowest odd mode. 28. Stream lines of fluid motion associated with the magnetic field oscillation of the lowest odd mode. 30. Stream lines of fluid motion associated with the magnetic field oscillation of the lowest even mode.
H . D . disturbance grows indefinitely if the steady T | and Γ 2 fields are larger than the steady Sx field. Such a conclusion seemed to conflict with the supposed existence of a strong toroidal field. The influence of the earth's rotation on the stability was next taken into account ( R I K I T A K E , 1956b), and the last equation of (4-8) was replaced by: gdv/dt + 2ρ(ω0 A V) = i A H0 + I0 A h — grad> (4-41) After a treatment similar to the case of a rotating sphere in an external field, it turned out that the effect of the Coriolis force is so large that M .
D . D. O S C I L L A T I O N S OF A PERFECTLY CONDUCTING FLUID SPHERE 49 of the small disturbance given to the system. F o r a fluid supposed in the earth's core, incompressibility may be further assumed, so that we add: divv = 0 (4-9) to (4-8). If we suppose a fluid body with no motion as well as no electric current at its equilibrium state, (4-8) is simplified as : ι = a(e + ν A i / 0) curie = —dh/dt (4-10) curl/z = 4πι qdv/dt = i A H0 — grad/? the magnetic field H0 being externally applied to the system in this case.