Ebru Devlen, Axel Brandenburg, Dhrubaditya Mitra
Using direct numerical simulations, we demonstrate that "flow IV" of Roberts (1972) exhibits dynamo action dominated by horizontally averaged large-scale magnetic field. With the test-field method we show that the magnetic eddy diffusivity is negative and overcomes the molecular diffusivity to explain this large-scale dynamo for magnetic Reynolds numbers above $\approx8$. As expected for a dynamo of this type, the two horizontal field components grow independently of each other and have arbitrary amplitude ratios and phase differences. Small length scales of the mean magnetic field are shown to be stabilized by the eddy diffusivity becoming positive at wavenumbers larger than twice the characteristic wavenumber of the flow. For magnetic Reynolds numbers below $\approx0.5$ the eddy diffusivity is confirmed to be positive, as expected for all incompressible flows. Earlier claims of a dynamo driven by a modified Taylor-Green flow through negative eddy diffusivity could not be confirmed.
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http://arxiv.org/abs/1212.2626
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