A new simulation set-up is proposed for studying mean field dynamo action .
The model combines the computational advantages of local cartesian geometry with the ability to include a shear profile that resembles the sun ’ s differential rotation at low latitudes .
It is shown that in a two-dimensional mean field model this geometry produces cyclic solutions with dynamo waves traveling away from the equator – as expected for a positive alpha effect in the northern hemisphere .
In three dimensions with turbulence driven by a helical forcing function , an alpha effect is self-consistently generated in the presence of a finite imposed toroidal magnetic field .
The results suggest that , due to a finite flux of current helicity out of the domain , alpha quenching appears to be non-catastrophic – at least for intermediate values of the magnetic Reynolds number .
For larger values of the magnetic Reynolds number , however , there is evidence for a reversal of the trend and that \alpha may decrease with increasing magnetic Reynolds number .
Control experiments with closed boundaries confirm that in the absence of a current helicity flux , but with shear as before , alpha quenching is always catastrophic and alpha decreases inversely proportional to the magnetic Reynolds number .
For solar parameters , our results suggest a current helicity flux of about 0.001 { G ^ { 2 } / s } .
This corresponds to a magnetic helicity flux , integrated over the northern hemisphere and over the 11 year solar cycle , of about 10 ^ { 46 } { Mx } ^ { 2 } .