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(b) the hydrodynamic equations, including conservation of mass and momentum and the
equation of motion for the fluid in the outer core;
(c) the thermal equations governing the transfer of heat in a flowing fluid or the similar
equations governing compositional convection; and
(d) the boundary and initial conditions.
Simultaneous solution of all these equations is exceedingly difficult, in part
because the equations are non-linear. However, in special situations solutions
can be found for some of the equations. One such simplified approach is to
assume a velocity field for the flow in the outer core and then to solve the elec-
tromagnetic equations of group (a) to see what type of magnetic field it would
generate. Another line of work has been to investigate group (b), possible fluid
motions in a fluid outer core sandwiched between a solid mantle and a solid
inner core. Figure 8.25 shows the fluid motions observed in a scaled laboratory
experiment using a rotating spherical model, with the fluid outer core subjected to
a temperature gradient. The convection cells in this model core were cylindrical
rolls, with the fluid spiralling in opposite directions in the northern and southern
hemispheres. The Coriolis force means that the rolls are aligned with the rotation
axis. The dynamics of the flow are significantly affected by the inner core: the
rolls are unstable close to the axis and can touch the inner core. The problem
with applying flow patterns such as these directly to dynamo models is that any
flow pattern is markedly altered by the magnetic field it generates. Figure 8.26
shows schematically the interaction between magnetic field and fluid flow for one
dynamo model, the Parker-Levy dynamo. For this particular dynamo model to
be self-sustaining, four conditions must be satisfied.
1. The initial dipole field must be aligned along the Earth's spin axis.
2. The fluid outer core must be rotating.
3. There must be upwelling thermal convection currents in the outer core.
4. A spiralling motion of the convection system caused by the Coriolis force is required.
The spiralling motions have opposite polarities in the northern and southern hemi-
spheres.
The rotation of the electrically conducting fluid in the outer core will stretch
the original dipole magnetic-field lines and wind them into a toroidal field. The
interaction of this toroidal magnetic field with the convecting rolls then results
in a magnetic field with loops that are aligned with the rotation axis. If the loops
have the same sense as the original field, that dipole field can be regenerated; but
if the loops have the opposite sense, the original dipole field can be reversed.
Although it can be shown that a convecting outer core can act as a dynamo
that undergoes intermittent polarity reversals, exactly why these reversals occur
is not clear. They could be due to the random character of the irregular fluid
convection and the non-linear coupling of the fluid motion with the magnetic
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