Variational methods and core modes - Earth Dynamics: Deformations and Oscillations of the Rotating Earth - page 464

Azimuthal component Meridional projection

Rotation
axis

Equator

Figure 8.6 Flow vector field for the spin-over mode in a spherical Earth model.

nutation was first predicted by Poincare (1910) for a completely fluid, incompress-
ible core bounded by a rigid shell. In a variational calculation of wobble-nutation
modes in realistic Earth models, Jiang (1993) found the classical retrograde free
core nutation (RFCN), but discovered a prograde free core nutation (PFCN) as
well. Observation of these two modes is described in Section 4.4.2. For the PFCN,
the accompanying nearly diurnal retrograde wobble has a period slightly longer
than a sidereal day, while for the RFCN the accompanying wobble has a period
slightly shorter than a sidereal day. The flow vector field for the spin-over mode is
plotted in Figure 8.6.
The solid inner core of the Earth is held in its central position by relatively weak
gravitational forces. The weakness of this equilibrium is reflected in the very large
degree-one internal load Love numbers for the inner core, as listed in Tables 7.1
and 7.2. This results in an axial translational mode for the inner core. The gen-
eralised displacement potential for this mode is shown in Figure 8.7. It is axially
symmetric and odd with respect to the equatorial plane. The motion in this mode
is principally in the direction of the rotation axis, so it is not much a ected by

the Coriolis acceleration. The displacement vector field is plotted in Figure 8.8.
The azimuthal component for this mode is quite small, as shown on the left side of
the plot. The motion is largely in the meridional plane, as shown on the right side
of the plot.
The motion of the inner core can also be parallel to the equatorial plane. In
this case, the Coriolis acceleration is a maximum and the mode is split into two
motions, one rotating in the equatorial plane in the prograde sense and the other
rotating in the equatorial plane in the retrograde sense. The azimuthal number for
these two modes is unity and the generalised displacement potential is even in the

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