$\alpha$ Effect in a Family of Chaotic Flows

We perform numerical experiments to calculate the kinematic $\alpha$ effect for a family of maximally helical, chaotic flows with a range of correlation times. We find that the value of $\alpha$ depends on the structure of the flow, on its correlation time and on the magnetic Reynolds number in a nontrivial way. Furthermore, it seems that there is no clear relation between $\alpha$ and the helicity of the flow, contrary to what is often assumed for the parametrization of mean-field dynamo models.

Figure 1

Typical temporal evolution of $⟨\mathit{u}\times \mathit{b}{⟩}_x$ for flow (9) with $ϵ=0.75$, $Rm=64$, $B_0=1$.

Figure 2

Dependence of $\alpha$ and $\gamma$ on $Rm$ for flow (9) for different values of $ϵ$.

Figure 3

$⟨\mathbf{u}\times \mathbf{b}{⟩}_x$ as a function of time for flow (10) with $Rm=64$, $ϵ=0.75$, and ${\tau }_c=3.75$ (top), ${\tau }_c=37.5$ (bottom).

Figure 4

Dependence of $\alpha$ and $\gamma$ on $Rm$ for flow (10) for different values of ${\tau }_c$ and $ϵ=0.75$.