On magnetic field generation in Kolmogorov turbulence
Abstract
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) ~ l^alpha, alpha<1. We propose that: (i) In the limit of small 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 the Kolmogorov turbulence with small Prandtl numbers need to achieve extremely high resolution in order to adequately describe magnetic phenomena; (ii) For small Prandtl numbers, magnetic energy penetrates below the resistive scale and has a power-law spectrum between the resistive and viscous scales. Magnetic energy is dissipated not at the resistive scale but at the much smaller viscous scale, which may be relevant for the problems of anomalous resistivity and fast magnetic reconnection. Our results also suggest that the level of magnetic energy saturation depends on the Prandtl number.Keywords
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