Catastrophic alpha quenching alleviated by helicity flux and shear

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.