Scaling laws in decaying helical hydromagnetic turbulence

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)