The helicity constraint in turbulent dynamos with shear

The evolution of magnetic fields is studied using simulations of forced hel ical turbulence with strong imposed shear. After some initial exponential g rowth, the magnetic field develops a large-scale travelling wave pattern. T he resulting field structure possesses magnetic helicity, which is conserve d in a periodic box by the ideal magnetohydrodynamics equations and can hen ce only change on a resistive time-scale. This strongly constrains the grow th time of the large-scale magnetic field, but less strongly constrains the length of the cycle period. Comparing this with the case without shear, th e time-scale for large-scale field amplification is shortened by a factor Q , which depends on the relative importance of shear and helical turbulence, and which also controls the ratio of toroidal to poloidal field. The resul ts of the simulations can be reproduced qualitatively and quantitatively wi th a mean-field alpha Omega -dynamo model with alpha-effect and turbulent m agnetic diffusivity coefficients that are less strongly quenched than in th e corresponding a alpha (2)-dynamo.