Scaling laws in decaying helical hydromagnetic turbulence

✍ Scribed by M. Christensson; M. Hindmarsh; A. Brandenburg

• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 165 KB
• Volume: 326
• Category: Article
• ISSN: 0004-6337
• DOI: 10.1002/asna.200510365

✦ Synopsis

Abstract

We study the evolution of growth and decay laws for the magnetic field coherence length ξ, energy E~M~ and magnetic helicity H in freely decaying 3D MHD turbulence. We show that with certain assumptions, self‐similarity of the magnetic power spectrum alone implies that ξ ∼ t^1/2^. This in turn implies that magnetic helicity decays as H ∼ t^–2__s__^, where s = (ξ~diff~/ξ~H~)^2^, in terms of ξ~diff~, the diffusion length scale, and ξ~H~, a length scale defined from the helicity power spectrum. The relative magnetic helicity remains constant, implying that the magnetic energy decays as E~M~ ∼ t^–1/2–2__s__^. The parameter s is inversely proportional to the magnetic Reynolds number Re~M~, which is constant in the self‐similar regime. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)