Scaling laws in decaying helical hydromagnetic turbulence

We study the evolution of growth and decay laws for the magnetic field coherence length, 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 similar to t(1/2). This in turn implies that magnetic helicity decays as H similar to t(-2s), where s = (xi(diff)/xi(H))(2), in terms of xi(diff), the diffusion length scale, and xi(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 similar to t(-1/2-2s). The parameter s is inversely proportional to the magnetic Reynolds number Re-M, which is constant in the self-similar regime.