Catastrophic alpha quenching alleviated by helicity flux and shear

¹ NORDITA, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark e-mail: brandenb@nordita.dk
² Astrophysical Institute Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany e-mail: CSandin@aip.de

Received: 16 January 2004
Accepted: 21 July 2004

Abstract

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 α 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 . This corresponds to a magnetic helicity flux, integrated over the northern hemisphere and over the 11 year solar cycle, of about .