Graeme Morrison and David R. Fearn

This study assesses the influence of different prescribed parameters on the solutions of a 2.5D hydromagnetic dynamo model. The numerical solution is fully resolved in r and q, but severely truncated in f so that only a single, prescribed value of the azimuthal wavenumber, m, is included in addition to the axisymmetric (m = 0) part of the problem. This model is ideally suited for such a study since it is a self-consistent, convectively driven dynamo, capable of reproducing qualitatively similar axisymmetric magnetic fields to those of a Boussinesq 3D model, but at considerably lower computational effort. We have chosen to vary the Rayleigh number, Ra, for m = 2 and m = 4, and we find that the solution is dependent on the choice of both Ra and m. This means that the 2.5D model is too severely truncated in f, and suggests that caution should be exercised when interpreting the results from a single run of any convectively driven numerical dynamo model, at a particular value of Ra. For m = 2, and all other parameters fixed, we have also investigated the effect of varying the inner core radius, giving some insight into possible effects of the growth of an inner core on magnetic field generation in planetary bodies. A stabilising effect on the magnetic field is unexpectedly observed for sufficiently small inner core radii. The anticipated stabilising effect is observed as our inner core radius increases from about its present value, until the dynamo shuts off for a radius ratio c, of about a half, for our fixed value of Ra.