Magnetic field generation in Kolmogorov turbulence

Physics

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Turbulent Flows

Scientific paper

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) ~ lα, α < 1. This regime is relevant to the problem of magnetic field generation in turbulent fluids with small magnetic Prandtl number, i.e. with ohmic resistivity much larger than viscosity. Our interest in motivated by the following question: suppose that smooth fluctuations of velocity field are able to amplify a weak magnetic field, would the magnetic field be still amplified if the fluid motion becomes strongly turbulent, i.e. non-smooth? Quite paradoxically, turbulence can be dangerous for magnetic field generation. We propose that the smaller the magnetic Prandtl number, the larger the magnetic Reynolds number that is needed to excite magnetic fluctuations. This implies that numerical or experimental investigations of magnetohydrodynamical turbulence with small Prandtl numbers need to achieve extremely high resolution in order to describe magnetic phenomena adequately.

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