Abstract
We study the generation of magnetic field by a helical flow made of a mean steady flow plus a fluctuating flow assumed to behave like a Gaussian white noise. The steady flow and the fluctuations are both solid body screw motions with constant pitches, respectively, and . The threshold shift induced by fluctuations of small amplitude is calculated analytically as a function of for different values of , m and k being the axial and azimuthal wavenumbers of the magnetic field. For a fixed value of , negative threshold shifts have been found provided belongs to a bounded interval . When there is no mean flow, the analysis is extended to temporal fluctuations modeled by a colored noise. In that case, emphasis is put on the influence of the correlation time on the dynamo onset.
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