David R. Fearn and Graeme Morrison
We investigate the effect of inertia in hydrodynamic
models of the geodynamo. To permit a reasonable survey of parameter space,
we use a 2.5D model (that is fully resolved in radius r and colatitude
q but which is highly truncated in azimuth;
including only the modes m=0 and m=m1 =2,
where m is the azimuthal wavenumber). Earlier work (Morrison and
Fearn 2000) considered the system in the absence of inertia. Here we include
the full inertial term and measure its strength with the Rossby number
Ro. For Ekman number E=10-3,
we have investigated dynamo solutions for Rossby numbers in the range 5
. 10-5 to 5 .10-4.
Our numerical method is not capable of exploring smaller values of Ro,
but the lower Ro results are consistent with the Ro=0 result
obtained by an independent, inertia-less code. At values of Ro greater
than the range indicated above, no dynamo solutions were found. The range
5 . 10-5 < Ro <5 .10-4
contains two solution branches: a weaker-field branch for Ro <
10-4 and a stronger-field branch
for Ro >10-4. The former
is oscillatory, the latter chaotic. The strength of the field generated
increases with Ro on the weaker-field branch but decreases with
increasing Ro on the stronger-field branch until at some (not precisely
determined) value of Ro greater than 5 . 10-4,
there is no field generation.