Small-scale helicity and α -effect in the Earth's core

Abstract

It is a commonly held belief that the combination of rotation and buoyancy creates a net helicity and electromotive force (EMF), known as an α -effect, and hence, dynamo action. We investigate this possibility for a simple, but dynamically complete, model, consisting of a small, isolated buoyant parcel rising in an infinite extent of rotating electrically conducting Boussinesq fluid in the presence of a large-scale magnetic field. We show that the leading order in the local magnetic Reynolds number, assumed small, is that the total helicity and EMF are identically zero, due to symmetry. This is in effect an anti-dynamo theorem, to be overcome if dynamo action is to occur. The helicity and EMF densities are found to be concentrated in wakes having spatial extent much larger than the scale of the buoyant parcel. The wakes are aligned with rotation if Coriolis force dominates Lorentz (forming a foreshortened Taylor column) and with the magnetic field if Lorentz dominates Coriolis. Consequently, the integrals of helicity and EMF over a half-space on either side of the parcel are non-zero. These distributions have the potential of creating wavelike dynamo action as the buoyant parcel rises through the outer core. In the case that the Coriolis force is dominant and the viscous force is very weak, it is found that the half-space integral of helicity is inversely proportional to the square root of the Ekman number. This is a counterintuitive result, depending on the action of a very weak viscous force at very large distance from the buoyant parcel.