Growth of a Weak Magnetic Field in a Turbulent Conducting Fluid with Large Magnetic Prandtl Number

Abstract

The behavior of a weak fluctuating magnetic field in a turbulent electrically conducting fluid with large magnetic Prandtl number is re-examined, without using vorticity analogy. For large magnetic Prandtl number, the characteristic length of the small eddies of turbulence is much larger than that of the small loops of the magnetic field. By inferring that the small eddies of turbulence are mainly responsible for the change of the fluctuation intensity of the magnetic field and by utilizing Batchelor's mixing approach, visualizing the turbulent velocity field as effectively a rather persistent uniform straining motion for the small-scale variation of magnetic field, it was found that the fluctuation intensity of the magnetic field grows due to turbulent motion for very large magnetic Prandtl number [(ν/λ) > 100, say] and approaches a constant value asymptotically. The rate of growth is found to be a function of ν/λ and τ (the product of time and the turbulent straining rate).