Three processes of inducing the steady poloidal field in the Earth's core.

Abstract

When the magnetic field and the fluid velocity in the Earth's core are expressed by toroidal and poloidal modes, four types of interaction are conceivable between them: interaction of (a) poloidal velocity (νS) with poloidal magnetic field (BS) [νS×BS]; (b) poloidal velocity with toroidal field (BT) [νS×BT]; (c) toroidal velocity (νT) with poloidal field [νT×BS]; and (d) toroidal velocity with toroidal field [νT×BT]. The last type of interaction [νT×BT] does not induce any poloidal magnetic field. We therefore examine the first three types of interaction that induce the poloidal magnetic fields, which are to be compared with the observed non-dipole field.If we assume a dipole field and a toroidal field of the second degree and order zero, the first two types of interaction, the poloidal-poloidal interaction [νS×BS] and the poloidal-toroidal interaction [νS×BT], induce two modes of poloidal field, (l-1, k) and (l+1, k), from the velocity of the (l, k) mode. When a plausible radial function is assumed for the velocity, the lower mode (l-1, k) always predominates, indicating that the lower mode is more easily observable.Among the three types of interaction, the poloidal-poloidal interaction [νS×BS] is the most efficient for inducing the poloidal field, giving the largest amplitude of the induced field for the same magnitude of the velocity and the primary field. The amplitude of the field which is induced by the poloidal-toroidal interaction [νS×BT] and the toroidal-poloidal interaction [νr×BS] decreases with increasing velocity, if the magnitude of the velocity is constant irrespective of the degree of the velocity. The decrease is the steepest with the toroidal-poloidal interaction. If we ascribe the cause of the standing field to this type of interaction, the velocity of higher harmonics should be predominant in the core, because the observed slope of decrease for the standing field is less steep than that calculated for the constant velocity. On the other hand, if we assume other interactions, the velocity of the lower harmonics should be predominant.