2 Short title : LARGE - SCALE MAGNETIC FIELD GENERATION GENERATION OF MULTISCALE MAGNETIC FIELD BY PARITY - INVARIANT TIME - PERIODIC FLOWS

We study generation of magnetic fields involving large spatial scales by time-and space-periodic small-scale parity-invariant flows. The anisotropic magnetic eddy diffusivity tensor is calculated by the standard procedure involving expansion of magnetic modes and their growth rates in power series in the scale ratio. Our simulations, conducted for flows with random harmonic composition and exponentially decaying energy spectra, demonstrate that enlargement of the spatial scale of magnetic field is beneficial for generation by time-periodic flows. However, they turn out, in general, to be less efficient dynamos, than steady flows. 1 The present work is an extension of the studies carried out by Lanotte et al. (2000) and Zheligovsky et al. (2001), who found steady parity-invariant flows with a negative magnetic eddy diffusivity to be quite common. A similar investigation for turbulent flows is desirable, especially given that flows in experimental dynamos are necessarily turbulent (see discussion ibid.). Some time-dependent flows are known to be unable to sustain negative magnetic eddy diffusivity – namely, the flows, δ-correlated in time at each point in space. They advect a mean magnetic field as a passive scalar, and therefore eddy diffusivity can only exceed molecular diffusivity (Biferale et al. , 1995). Thus the question, whether time-dependent flows can give rise to negative magnetic eddy diffusivity, is not trivial. However, dynamo simulations for time-dependent turbulent flows are numerically demanding. For this reason we focus our attention here at an " intermediate " class of flows – those periodic in time, and employ the simplest of them: v(x, t) = U(x) + √ ω(V c (x) cos ωt + V s (x) sin ωt). (1) Like in the cited papers, a flow is supposed to be 2π-periodic in spatial variables x and parity-invariant, i.e. v(x, t) = −v(−x, t). (2) Consequently, its space-averaged helicity is zero, and no α-effect is present. Two families of space-and time-periodic flows were closely examined in the context of fast kinematic magnetic dynamo theory. Both are general-isations of ABC flows, and flows from both families are constructed of a small number of spatial Fourier harmonics. A flow of the kind of " modulated waves " , proposed by Otani (1993) and studied also by Childress & Gilbert (1995), has the form (1). " Circularly polarised " flows were employed in simulations by Galloway & Proctor (1992) and Galloway & O'Brian (1993); for near-integrable flows of this kind analytical results were presented …