Abstract
We study the effect of stochastic velocity fluctuations on 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. We calculate analytically, the threshold shift and the frequency shift induced by fluctuations of small amplitude that are geometrically optimized. It is found that the threshold is lowered, provided the steady part of the flow represented by a solid body screw motion with constant pitch satisfies the condition where m and k, respectively, are the axial and azimuthal wavenumbers of the magnetic field such that m = −k = 1. When there is no mean flow we extend the analysis to fluctuations with a finite correlation time and find that the dynamo threshold is higher than for a steady flow with the same geometry.
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