Scaling laws in decaying helical hydromagnetic turbulence

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We study the evolution of growth and decay laws for the magnetic field coherence length xi, energy Eₘ 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 xi t¹/². This in turn implies that magnetic helicity decays as H t⁻²ˢ, where s=(xidiff/xiₕ)², in terms of xidiff, the diffusion length scale, and xiₕ, a length scale defined from the helicity power spectrum. The relative magnetic helicity remains constant, implying that the magnetic energy decays as Eₘ t⁻¹/²⁻²ˢ. The parameter s is inversely proportional to the magnetic Reynolds number Reₘ, which is constant in the self-similar regime.