Can catastrophic quenching be alleviated by separating shear and alpha effect?

The small-scale magnetic helicity produced as a by-product of the large-scale dynamo is believed to play a major role in dynamo saturation. In a mean-field model the generation of small-scale magnetic helicity can be modelled by using the dynamical quenching formalism. Catastrophic quenching refers to a decrease of the saturation field strength with increasing Reynolds number. It has been suggested that catastrophic quenching only affects the region of non-zero helical turbulence (i.e. where the kinematic alpha operates) and that it is possible to alleviate catastrophic quenching by separating the region of strong shear from the alpha layer. We perform a systematic study of a simple axisymmetric two-layer alpha-omega dynamo in a spherical shell for Reynolds numbers in the range 1 < Rm < 10^5. In the framework of dynamical quenching we show that this may not be the case, suggesting that magnetic helicity fluxes would be necessary.