Magnetic-Field Generation in Kolmogorov Turbulence

We analyze the initial, kinematic stage of magnetic field evolution in an isotropic and homogeneous turbulent conducting fluid with a rough velocity field, $v(l)\sim l^{\alpha }$, $\alpha <1$. This regime is relevant to the problem of magnetic field generation in fluids with small magnetic Prandtl number, i.e., with Ohmic resistivity much larger than viscosity. We propose that 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.