Slow oscillations of fluid in a rotating cavity in the presence of a toroidal magnetic field

Hide (1966) has suggested that the slow westward drift of the non-dipole components of the Earth’s magnetic field may be caused by slow free oscillations of the fluid part of the Earth’s core in the presence of a dominant toriodal magnetic field. An attempt is made here to analyse this suggestion in detail. First, slow (or second class oscillations in a thin shell are examined in the presence of a uniform toroidal field and Hide’s theory is shown to be qualitatively correct but to underestimate the actual periods of oscillation. In these oscillations the drift is to the east and Hide argued that for a thick shell there will be a change of sign in the drift in conformity with observation. Accordingly the present theory is extended to thick shells, but it is shown that, for those oscillations in (1-1) correspondence with the ones already found for a thin shell, no such change of sign occurs. Since such oscillations are as likely to be manifested on the exterior field as any other it is concluded that the analysis presented here raises a serious objection to Hide’s proposal. It is noted, however, that for some higher modes of oscillation a drift to the west is almost certain.