The role of inertia in hydrodynamic models of the geodynamo

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 θ 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 (Phy. Earth Planet. Inter. 117 (2000) 237) considered the system in the absence of inertia. Here, we include the full inertial term and measure its strength with the magnetic Ekman number Eη. For Ekman number E=10−3, we have investigated dynamo solutions for magnetic Ekman numbers in the range 5×10−5 to 5×10−4. Our numerical method is not capable of exploring smaller values of Eη, but the lower Eη results are consistent with the Eη=0 result obtained by an independent, inertia-less code. At values of Eη greater than the range indicated above, no dynamo solutions were found. The range 5×10−5 [less,approximate] Eη [less, approximate] 5×10−4 contains two solution branches: a weaker-field branch for Eη [less, approximate] 10−4 and a stronger-field branch for Eη [greater than or equivalent to] 10−4. The former is oscillatory, the latter chaotic. The strength of the field generated increases with Eη on the weaker-field branch but decreases with increasing Eη on the stronger-field branch until at some (not precisely determined) value of Eη greater than 5×10−4, there is no field generation