Negative magnetic eddy diffusivity due to oscillogenic $\alpha$-effect

TL;DR

This paper investigates how certain mirror-antisymmetric flows can induce large-scale magnetic field oscillations and negative eddy diffusivity, leading to dynamo action without growth or decay, using asymptotic multiscale stability analysis.

Contribution

It demonstrates that magnetic $ ext{α}$-effect in such flows causes harmonic oscillations and negative eddy diffusivity, revealing a new dynamo mechanism with anisotropic effects.

Findings

Flows act as kinematic dynamos on the scale O(ε²t).

Eddy diffusivity exhibits singular behavior and can be negative.

Numerical analysis confirms the dynamo mechanism in sample flows.

Abstract

We study large-scale kinematic dynamo action of steady mirror-antisymmetric flows of incompressible fluid, that involve small spatial scales only, by asymptotic methods of the multiscale stability theory. It turns out that, due to the magnetic $\alpha$-effect in such flows, the large-scale mean field experiences harmonic oscillations in time on the scale O($\varepsilon t$) without growth or decay. Here $\varepsilon$ is the spatial scale ratio and $t$ is the fast time of the order of the flow turnover time. The interaction of the accompanying fluctuating magnetic field with the flow gives rise to an anisotropic magnetic eddy diffusivity, whose dependence on the direction of the large-scale wave vector generically exhibits a singular behaviour, and thus to negative eddy diffusivity for whichever molecular magnetic diffusivity. Consequently, such flows always act as kinematic dynamos on the time scale O($\varepsilon^2t$); for the directions at which eddy diffusivity is infinite, the large-scale mean-field growth rate is finite on the scale O($\varepsilon^{3/2}t$). We investigate numerically this dynamo mechanism for two sample flows.