Plot of the real part of the eigenvalue for the fastest growing magnetic field mode as a function of the magnetic Reynolds number Rm (using logarithmic scale in the x axis).
Time evolution of the magnetic energy, which highlights the information provided by transient behaviours. (a) a simulation for Rm = 16.5 (<Rm1) using as initial condition the final solution obtained at Rm > Rm1, (b) simulation for Rm = 28.4 (>Rm1).
Plot of the imaginary part of the eigenvalue as a function of Rm (using logarithmic scale in the x axis).
Phase space diagrams for Rm < Rm1 (a) and Rm > Rm1 (b).
Eigenvalues coalescence for Rm close to Rm2 ≃ 215. Both the real part (written as σ(Rm) − σ2) and the opposite of the imaginary part (i.e., −ω(Rm)) are represented (a). The sum F of both (b), and sign (Rm − Rm2)F 2 illustrate the continuity and regularity in the functional form of the eigenvalue (see text).
Evolution in time of the projection of the dominant mode on the two large scale components, represented via the angle θ, such that .
Eigenmode obtained for Rm = 434.2 (>Rm2). An isosurface of the magnetic energy is represented. To highlight the symmetry, it is coloured according to the value of B x , from negative (dark gray – blue online) to positive (lighter gray – red online). The corresponding eigenvalue is purely real, yet the double cigars structure of the field remains clearly visible. Magnetic field lines are also depicted on the right plot.
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