Modeling spatio-temporal nonlocality in mean-field dynamos

TL;DR

This paper extends the modeling of mean-field dynamos to cases with poor spatial and temporal scale separation by incorporating integral kernels, enabling more accurate simulations of oscillatory dynamo behavior.

Contribution

It generalizes the test-field method to include both spatial and temporal nonlocality, deriving a PDE approach for the mean electromotive force.

Findings

Oscillatory dynamos have lower critical dynamo numbers.

The integral kernel approach simplifies modeling nonlocal effects.

Oscillatory alpha-shear and alpha^2 dynamos are effectively simulated.

Abstract

When scale separation in space and time is poor, the alpha effect and turbulent diffusivity have to be replaced by integral kernels. Earlier work in computing these kernels using the test-field method is now generalized to the case in which both spatial and temporal scale separations are poor. The approximate form of the kernel is such that it can be treated in a straightforward manner by solving a partial differential equation for the mean electromotive force. The resulting mean-field equations are solved for oscillatory alpha-shear dynamos as well as alpha^2 dynamos in which alpha is antisymmetric about the equator, making this dynamo also oscillatory. In both cases, the critical values of the dynamo number is lowered by the fact that the dynamo is oscillatory.