Dynamic Nonlinearity in Large‐Scale Dynamos with Shear

We supplement the mean field dynamo growth equation with the total magnetichelicity evolution equation. This provides an explicitly time dependent modelfor alpha quenching in dynamo theory. For dynamos without shear, this approachaccounts for the observed large scale field growth and saturation in numericalsimulations. After a significant kinematic phase, the dynamo is resistivelyquenched, i.e. the saturation time depends on the microscopic resistivity. Thisis independent of whether or not the turbulent diffusivity is resistivelyquenched. We find that the approach is also successful for dynamos that includeshear and exhibit migratory waves (cycles). In this case however, whether ornot the cycle period remains of the order of the dynamical time scale at largemagnetic Reynolds numbers does depend how on how the turbulent magneticdiffusivity quenches. Since this is unconstrained by magnetic helicityconservation, the diffusivity is presently an input parameter. Comparison tocurrent numerical experiments suggests a turbulent diffusivity that dependsonly weakly on the magnetic Reynolds number, but higher resolution simulationsare needed.Comment: 21 pages, 5 figures (revised version