Mixed-parity Solutions in a Mean-field Dynamo Model

S u m m a r y : We consider the effect of including both dipole and quadrupole parities in the previous mean-field model of Hollerbach and Jones (1995), which considered dipole parity only. Allowing for both parities, we find that the onset of dynamo action occurs at a0 « 6, in the form of a purely quadrupolar dynamo wave. A symmetry-breaking bifurcation then occurs at ao « 11, beyond which the solutions are of mixed parity. The quadrupolar component still oscillates about a zero time-average, but the dipolar component about a non-zero average. For even greater aco we obtain an unconnected upper-branch solution. In sharp contrast to the HJ95 pure-parity upper branch, however, this mixed-parity upper branch is steady-state rather than periodic. Although it does not appear to be possible to connect these two upper branches by any simple sequence of bifurcations, we nevertheless suggest how aspects of the mixed-parity branch may help in understanding features of the previous pure-parity branch.