Magnetic helicity fluxes in interface and flux transport dynamos

Abstract

Context. Dynamos in the Sun and other bodies tend to produce magnetic fields that possess magnetic helicity of opposite sign at large and small scales, respectively. The build-up of magnetic helicity at small scales provides an important saturation mechanism. Aims. In order to understand the nature of the solar dynamo we need to understand the details of the saturation mechanism in spherical geometry. In particular, we aim to understand the effects of magnetic helicity fluxes from turbulence and meridional circulation. Methods. We consider a model with only radial shear confined to a thin layer (tachocline) at the bottom of the convection zone. The kinetic α owing to helical turbulence is assumed to be localized in a region above the convection zone. The dynamical quenching formalism is used to describe the build-up of mean magnetic helicity in the model, which results in a magnetic α effect that feeds back on the kinetic α effect. In some cases we compare these results with those obtained from a model with a simple algebraic α quenching formula.Results. In agreement with earlier findings, the magnetic α effect has the opposite sign compared with the kinetic α effect and leads to a catastrophic decrease of the saturation field strength proportional to the inverse magnetic Reynolds number. At high latitudes this quenching effect can lead to secondary dynamo waves that propagate poleward because of the opposite sign of α. These secondary dynamo waves are driven by small-scale magnetic helicity instead of the small-scale kinetic helicity. Magnetic helicity fluxes both from turbulent mixing and from meridional circulation alleviate catastrophic quenching. Interestingly, supercritical diffusive helicity fluxes also give rise to secondary dynamo waves and grand minima-like episodes.

Dynamical quenching with non‐local α and downward pumping

“…The model of Kitchatinov & Olemskoy (2011) contains an important feature that is found here only in timedependent cases, namely the sign reversal of α M in some places, which leads to catastrophic anti-quenching (or amplification). Similar sign reversals of the local value of α M have been seen in some earlier models with a local α effect Chatterjee et al 2011), but it needs to be seen whether this behavior is physically realistic and still compatible with the original equations.…”

Shear-driven and diffusive helicity fluxes in αΩ dynamos

“…This implies that in the region around ±45° the dynamo action is driven by the magnetic α effect. A similar secondary dynamo is found to be working for a different distribution of shear and α K (Chatterjee et al 2010b). As with PF boundary condition, large values of C VC result in a numerical instability of the magnetic field in the simulation with VF.…”

“…An interesting question is whether the quenching of the dynamo is catastrophic when both layers are segregated, as in the Parker's interface dynamo or the flux‐transport dynamo models. We address this question in detail in two companion papers (Chatterjee et al 2010a,b).…”

“…We consider models with either radial or latitudinal shear. The effects of meridional circulation will be investigated in detail in a companion paper (Chatterjee, Guerrero & Brandenburg 2010b).…”

Modeling spatio‐temporal nonlocality in mean‐field dynamos

“…However, in mean-field models the magnetic fields show frequently variations on scales much smaller than this. Chatterjee et al (2011a), discussed the small-scale fields at the bottom of the convection zone in their simulations of a mean-field dynamo model as an artifact of the neglect of nonlocality in space, but no solution to this problem was feasible at the time.…”