Spatio-temporal non-localities in a solar-like mean-field dynamo

Abstract

ABSTRACT The scale separation approximation, which is in the base of the solar mean-field dynamo models, can be hardly justified both by observations and theoretical applications to astrophysical dynamos. The general expression for the mean turbulent electromotive force can be written in integral form with convolution of the turbulent effects and mean magnetic field variations over scales of the turbulent flows and global scales of the mean-field dynamo. Following results of direct numerical simulations (DNS), which had been reported earlier, we take the Lorentzian form of the integral convolution kernels as an experimental fact. It allows us to approximate the governing equation for the mean electromotive force by the reaction–diffusion type equation. Solution of the eigenvalue problem reveals a few curious properties of the dynamo model with the non-local mean electromotive force. We find a decrease of the critical dynamo instability threshold, and an increase the dynamo periods of the unstable modes, as reported in earlier studies. Simultaneously, the non-local model shows substantially lower growth rate of the unstable dynamo modes in proximity of the critical threshold than the model which employs the scale separation approximation. We verify these findings using the non-linear solar dynamo model. For the supercritical regime, when the α-effect magnitude is about twice of the instability threshold, the model shows the Parker’s dynamo wave solutions with the wave propagating from the mid-latitude at the bottom of the convection zone towards the solar equator at the surface.