6. Three dimensional calculations
In this section we discuss only results obtained using the Model I velocities. We attempted to compare the results described in Sect. 5.1, obtained by using the 2D code, with those from a comparable calculation, for the same velocity data, using the 3D code. After some experimentation we adopted parameter values , , , , cm2 s-1, kpc for the simulations described below. Thus the value of in is cm2 s-1. It is plausible that the halo values of may be rather larger than cm2 s-1, but we chose the above value for computational convenience (smaller values of require a finer z -mesh). However our results are not very sensitive to the precise values of these parameters. We set , close to, but a little reduced from, the nominal value, of 3.75 and corresponds to a maximum value of of 1.5 km s-1 at . The integration grid had NI = NJ = 101, NK = 41.
The code was run for approximately 2 Gyr using the Method 1 reduction of the raw velocity data. For these calculations we used the velocity field mentioned in Sect. 5.1in connection with Fig. 3, that is a slightly modified form of that used for the majority of the calculations using the 2D dynamo code. The evolution of the global energies in the azimuthal modes is shown in Fig. 6, (the normalization cannot be directly compared with that of the two dimensional calculations), and Fig. 7 gives projections of the magnetic field vectors onto planes for several heights above the disc plane at time 1.2 Gyr. (Note that the length of the arrows representing the magnetic field vectors have been normalized to the maximum field strength present in each plot, and so the figures cannot be used directly to compare field strengths at different values of z.) A 2D calculation with broadly similar parameters ( kpc), except that cm2 s-1, can be used for comparison. The evolution of the modal energies is shown in Fig. 4, and can be compared with those shown in Fig. 6, and the field structure for this run at 1.2 Gyr, given in Fig. 8, can be compared with the various panels of Fig. 7. Although clearly the field structure in the 3D case does depend on z, and the diffusion is larger in that case, the plots in Figs. 4 and 6, and those in Figs. 7 and 8 possess sufficient similarities to suggest that little additional information on the structure of the fields is being revealed by the 3D simulation. Thus we did not pursue these 3D calculations further.
© European Southern Observatory (ESO) 1998
Online publication: December 16, 1997