On magnetic field generation in Kolmogorov turbulence

Astronomy and Astrophysics – Astrophysics

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In a turbulent highly conducting fluid, magnetic fields are amplified since the field lines are generally stretched by randomly moving fluid elements in which these lines are frozen. Such a mechanism of turbulent dynamo is expected to work in a variety of astrophysical systems (galaxy clusters, interstellar medium, stars, planets), is confirmed numerically, and is consistent with simple analytical models. Recently, there appeared the number of high-resolution numerical simulations of MHD turbulence with small magnetic Prandtl numbers [Pm=fluid viscosity/fluid resistivity], where magnetic fluctuations were not amplified. This revived old claims that dynamo does not exist in the Kolmogorov turbulence with Pm << 1. However, astrophysical observations show that magnetic fields are generated by turbulent motion rather effectively in planets and stars where magnetic Prandtl numbers are small (e.g., in the geo-dynamo, Pm=10-5, in stars, Pm= 0.01). The talk will address this apparent contradiction. I will argue that dynamo exists for any Pm, if the magnetic Reynolds number is large enough. Ref.: S. Boldyrev & F. Cattaneo, astro-ph/0310780.

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