Variational methods and core modes - Earth Dynamics: Deformations and Oscillations of the Rotating Earth - page 463

Azimuthal component Meridional projection

Rotation
axis

Equator

Figure 8.4 Flow vector field for the axisymmetric solution of the Poincare inertial
wave equation known as the (4,1,0) mode in the notation of Greenspan (1969,
p. 64). On the right the velocity vector is projected on the meridional plane, and
on the left the azimuthal component of velocity is shown in perspective on the
plane orthogonal to the meridional plane.

90

0

Radius

Figure 8.5 Generalised displacement potential for the spin-over mode in a spher-
ical Earth model. It has a period of 23.939 hours.

One of the most interesting core modes is the spin-over mode , which reflects
the ability of the outer core to rotate about an axis di erent from that of either the

inner core or the shell. It has a nearly diurnal period. The generalised potential for
this mode is illustrated in Figure 8.5. In the Earth frame of reference, this mode
produces the nearly diurnal retrograde wobble . In the space frame of reference
it is accompanied by the free core nutations . When the flattening of the bound-
aries of the fluid outer core and the figure-figure gravitational coupling are taken
into account, as well as the deformability of the boundaries, both a retrograde free
core nutation and a prograde free core nutation are found. The retrograde free core

ff