All Figures

$\begin{figure} \includegraphics[width=8cm]{9365fig1} \end{figure}$ Figure 1: Dependencies of the normalized $\alpha$ and $\eta _{\rm t}$ on $R_{\rm m}$ for the Roberts flow in the general case, i.e. independent of SOCA (solid lines), and in SOCA (dotted lines).
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In the text

$\begin{figure} \includegraphics[width=8cm]{9365fig2} \end{figure}$ Figure 2: Dependences of the normalized $\tilde{\alpha}$ and $\tilde{\eta}_{\rm t}$ on $k/k_{\rm f}$ for the Roberts flow with $R_{\rm m}=10/\sqrt {2}\approx 7.1$ (solid lines), compared with normalized SOCA results for $\tilde{\alpha} / R_{\rm m}$ and $\tilde{\eta}_{\rm t} / R_{\rm m}$ , which are independent of $R_{\rm m}$ (dotted lines).
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In the text

$\begin{figure} \includegraphics[width=8cm]{9365fig3}\end{figure}$ Figure 3: Normalized integral kernels $\hat{\alpha}$ and $\hat{\eta}_{\rm t}$ versus $k_{\rm f} \zeta$ for the Roberts flow with $R_{\rm m}=10/\sqrt {2}\approx 7.1$ (crosses), compared with normalized SOCA results for $\hat{\alpha} / R_{\rm m}$ and $\hat{\eta}_{\rm t} / R_{\rm m}$ , which are independent of $R_{\rm m}$ (dotted lines).
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In the text

$\begin{figure} \includegraphics[width=8cm]{9365fig4}\end{figure}$ Figure 4: Dependences of the normalized $\tilde{\alpha}$ and $\tilde{\eta}_{\rm t}$ on the normalized wavenumber $k/k_{\rm f}$ for isotropic turbulence forced at wavenumbers $k_{\rm f}/k_1=5$ with $R_{\rm m}=10$ (squares) and $k_{\rm f}/k_1=10$ with $R_{\rm m}=3.5$ (triangles), all with $\nu /\eta =1$ . The solid lines give the Lorentzian fits (35).
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In the text

$\begin{figure} \includegraphics[width=8cm]{9365fig5}\end{figure}$ Figure 5: Normalized integral kernels $\hat{\alpha}$ and $\hat{\eta}_{\rm t}$ versus $k_{\rm f} \zeta$ for isotropic turbulence forced at wavenumbers $k_{\rm f}/k_1=5$ with $R_{\rm m}=10$ (squares) and $k_{\rm f}/k_1=10$ with $R_{\rm m}=3.5$ (triangles), all with $\nu /\eta =1$ . The solid lines are defined by (36).
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In the text

$\begin{figure} \includegraphics[width=8cm]{9365fig6}\end{figure}$ Figure 6: Normalized growth rate $\lambda (k)$ for isotropic turbulence, calculated according to relation (38) with $\gamma = 3$ and with $\tilde{\eta}_{\rm t}/\eta_{\rm t0}$ and $\tilde{\alpha}/\alpha_0$ as given in (35), for $R_{\rm m}\to \infty$ (upper solid line), as well as $R_{\rm m}=10$ and 3.5 (next lower solid lines). For comparison, $\lambda$ is also shown for the case in which $\tilde{\eta}_{\rm t}/\eta_{\rm t0}$ coincides with $\tilde{\alpha}/\alpha_0$ as given in (35) (dotted lines), and for that of vanishing nonlocal effect in which $\tilde{\eta}_{\rm t}/\eta_{\rm t0} = \tilde{\alpha}/\alpha_0 = 1$ (dashed lines), each for the same three values of $R_{\rm m}$ .
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In the text

$\begin{figure} \includegraphics[width=8cm]{9365fig7}\end{figure}$ Figure 7: Mean magnetic field components $\overline {B}_x$ and $\overline {B}_y$ , normalized by the equipartition field strength $B_{\rm eq}$ , in the one-dimensional nonlinear dynamo model characterized in the text, for different values of $k_{\rm f}/ k_1$ and for vanishing nonlocal effects.
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In the text

$\begin{figure} \includegraphics[width=8cm]{9365fig1} \end{figure}$	Figure 1: Dependencies of the normalized $\alpha$ and $\eta _{\rm t}$ on $R_{\rm m}$ for the Roberts flow in the general case, i.e. independent of SOCA (solid lines), and in SOCA (dotted lines).
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$\begin{figure} \includegraphics[width=8cm]{9365fig2} \end{figure}$	Figure 2: Dependences of the normalized $\tilde{\alpha}$ and $\tilde{\eta}_{\rm t}$ on $k/k_{\rm f}$ for the Roberts flow with $R_{\rm m}=10/\sqrt {2}\approx 7.1$ (solid lines), compared with normalized SOCA results for $\tilde{\alpha} / R_{\rm m}$ and $\tilde{\eta}_{\rm t} / R_{\rm m}$ , which are independent of $R_{\rm m}$ (dotted lines).
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$\begin{figure} \includegraphics[width=8cm]{9365fig3}\end{figure}$	Figure 3: Normalized integral kernels $\hat{\alpha}$ and $\hat{\eta}_{\rm t}$ versus $k_{\rm f} \zeta$ for the Roberts flow with $R_{\rm m}=10/\sqrt {2}\approx 7.1$ (crosses), compared with normalized SOCA results for $\hat{\alpha} / R_{\rm m}$ and $\hat{\eta}_{\rm t} / R_{\rm m}$ , which are independent of $R_{\rm m}$ (dotted lines).
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$\begin{figure} \includegraphics[width=8cm]{9365fig4}\end{figure}$	Figure 4: Dependences of the normalized $\tilde{\alpha}$ and $\tilde{\eta}_{\rm t}$ on the normalized wavenumber $k/k_{\rm f}$ for isotropic turbulence forced at wavenumbers $k_{\rm f}/k_1=5$ with $R_{\rm m}=10$ (squares) and $k_{\rm f}/k_1=10$ with $R_{\rm m}=3.5$ (triangles), all with $\nu /\eta =1$ . The solid lines give the Lorentzian fits (35).
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$\begin{figure} \includegraphics[width=8cm]{9365fig5}\end{figure}$	Figure 5: Normalized integral kernels $\hat{\alpha}$ and $\hat{\eta}_{\rm t}$ versus $k_{\rm f} \zeta$ for isotropic turbulence forced at wavenumbers $k_{\rm f}/k_1=5$ with $R_{\rm m}=10$ (squares) and $k_{\rm f}/k_1=10$ with $R_{\rm m}=3.5$ (triangles), all with $\nu /\eta =1$ . The solid lines are defined by (36).
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$\begin{figure} \includegraphics[width=8cm]{9365fig7}\end{figure}$	Figure 7: Mean magnetic field components $\overline {B}_x$ and $\overline {B}_y$ , normalized by the equipartition field strength $B_{\rm eq}$ , in the one-dimensional nonlinear dynamo model characterized in the text, for different values of $k_{\rm f}/ k_1$ and for vanishing nonlocal effects.
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