Turbulent transport of vector (magnetic) field: intermittency and anomalous scalings

Numerous studies of magnetic fluctuations with a zero mean-field for small magnetic Prandtl numbers (Pr m ≪ 1) show that magnetic fluctuations cannot be generated by turbulent fluid flow with the Kolmogorov energy spectrum. In addition, the generation of magnetic fluctuations with a zero mean-field for Pr m ≪ 1 were not observed in numerical simulations. However, in astrophysical applications the magnetic Prandtl numbers are small and magnetic fluctuations are observed. Thus the mechanism of generation of magnetic fluctuations for Pr m ≪ 1 still remains poorly understood.