The effect of velocity fluctuations on the threshold of the dynamo effect, the magnetic induction, and also the non-linear behaviors in the saturation regime are analysed through a list of eight articles selected. These subjects are studied by numerical simulations in a three-dimensional periodic domain. Direct numerical simulation (DNS) and simulation using sub-grid scale modeling methods (LES), helped to highlight the effect of fluctuations on the threshold and many modes of dynamo in flows sustained with different forcings (Taylor-Green, ABC and G.O. Robert). In these systems in the saturation regime, non-linear effects appear, such as sub-critical bifurcations associated with hysteresis loops, and turbulent intermittent On-Off behaviors. A discussion and perspectives on these topics are presented, together with a long annexe describing the numerical methods and diagnostics that were used in this work.
