tokens: the dynamo action in astronomical bodies. We choose to work with periodic cuboid domains, because it allows us to study the dynamo properties of spatially periodic cellular flows. We vary the scale separation in the system through the reconstruction of the computational domain and the characteristic length-scale of the imposed velocity field. The first flow under consideration is the well-known ABC flow (named after Arnold, Beltrami Childress), recently reviewed by Galloway ( 2012 ). The second is a modulated version of the first, with imposed long-wavelength perturbation on the scale of the system. Such periodic flows are guaranteed to produce dynamo action for a wide range of finite values of R m (Roberts 1970 ). We study the kinematic dynamo action in domains of various aspect ratios, to examine the effect of changing the scale separation of the system as well as the effects of imposing a two-scale perturbed flow on the system in the kinematic regime. The first part (ABC flow) of the problem considered here has recently been investigated in a different way by Cameron Alexakis ( 2016 ), who carried out a theoretical study of kinematic dynamo using the Floquet formulation that was originally devised for the Mathieu equation (Whittaker Watson 1902 ). The authors adopted the concepts in Roberts ( 1970 ) to solve the induction equation in the presence of the ABC flow for arbitrary large-scale separations, showing a transition from a large- to small-scale dynamo through a change in the growth rate. The results from this analysis are in general agreement with the findings presented below as the scale separation becomes arbitrarily large. However, their paper does not include the results for Floquet waves with length-scales comparable to the size of the imposed flow, although Galanti, Sulem Pouquet ( 1992 ) noted that such eigenmodes play a crucial role in maintaining the dynamo for large R m . In this paper, we utilize a discrete wavenumber decomposition that is determined by the aspect ratio of the computational domain. This allows us to investigate the transition from a large- to small-scale dynamo with a special emphasis on the length-scale selection of the fastest growing eigenmode of magnetic field and focus on the comparison of the results from the classic ABC and the modulated perturbed flow cases. Our study is based on the results of numerical simulations using a pseudo-spectral method in a triply periodic domain and analytic estimates based on the scale-separation arguments. The choice of the imposed flows allows for the scenario wherein a large-scale dynamo would be obtained at the onset. We then vary magnetic diffusivity in order to study how the dynamo mechanism changes as we increase R m . There are two possibilities: (i) the large-scale structure is preserved due to either the large aspect ratio of the system or the imposed long-wavelength modulation; or (ii) the energy is passed from the large scales to the small scales as
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