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Magnetic fluctuations with a zero mean field in a random fluid flow with a finite correlation time and a small
Nathan Kleeorin1, Igor Rogachevskii, Dmitry Sokoloff
1Department of Mechanical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel.
Abstract:
Magnetic fluctuations with a zero mean field in a random flow with a finite correlation time and a small yet finite magnetic diffusion are studied. Equation for the second-order correlation function of a magnetic field is derived. This equation comprises spatial derivatives of high orders due to a nonlocal nature of magnetic field transport in a random velocity field with a finite correlation time. For a random Gaussian velocity field with a small correlation time the equation for the second-order correlation function of the magnetic field is a third-order partial differential equation. For this velocity field and a small magnetic diffusion with large magnetic Prandtl numbers the growth rate of the second moment of magnetic field is estimated. The finite correlation time of a turbulent velocity field causes an increase of the growth rate of magnetic fluctuations. It is demonstrated that the results obtained for the cases of a small yet finite magnetic diffusion and a zero magnetic diffusion are different.