NEGATIVE MAGNETIC EDDY DIFFUSIVITIES FROM THE TEST-FIELD METHOD AND MULTISCALE STABILITY THEORY
Alexander Andrievsky, Axel Brandenburg, Alain Noullez, Vladislav Zheligovsky · The Astrophysical Journal · 2015
The generation of a large-scale magnetic field in the kinematic regime in the absence of an α -effect is investigated by following two different approaches: the test-field method and the multiscale stability theory relying on the homogenization technique. Our computations of the magnetic eddy diffusivity tensor of the parity-invariant flow IV of G. O. Roberts and the modified Taylor–Green flow confirm the findings of previous studies and also explain some of their apparent contradictions. The two flows have large symmetry groups; this is used to considerably simplify the eddy diffusivity tensor. Finally, a new analytic result is presented: upon expressing the eddy diffusivity tensor in terms of solutions to auxiliary problems for the adjoint operator, we derive relations between the magnetic eddy diffusivity tensors that arise for mutually reverse small-scale flows and .