On magnetic field generation in Kolmogorov turbulence

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We analyze the initial, kinematic stage of magnetic field evolution in an isotropic and homogeneous turbulent conducting fluid with a rough velocity field, v(l) lᵃlpha, alpha<1. We propose that in the limit of small magnetic Prandtl number, i.e. when ohmic resistivity is much larger than viscosity, the smaller the roughness exponent, alpha, the larger the magnetic Reynolds number that is needed to excite magnetic fluctuations. This implies that numerical or experimental investigations of magnetohydrodynamic turbulence with small Prandtl numbers need to achieve extremely high resolution in order to describe magnetic phenomena adequately.