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We present a derivation of the time evolution equations for the energycontent of nonhelical magnetic fields and the accompanying turbulent flows fromfirst principles of incompressible magnetohydrodynamics in the generalframework of homogeneous and isotropic turbulence. This is then applied to theearly Universe, i.e., the evolution of primordial magnetic fields. Numericallyintegrating the equations, we find that most of the energy is concentrated atan integral wavenumber scale k_I where the turbulence turn over time equals theHubble time. At larger length scales L, i.e., smaller wavenumbers q = 2 \pi / L<< k_I, independent of the assumed turbulent flow power spectrum, mode-modecoupling tends to develop a small q magnetic field tail with a Batchelorspectrum proportional to the fourth inverse power of L and therefore a scalingfor the magnetic field of B ~ L^(-5/2).

Time Evolution of the Large-Scale Tail of Nonhelical Primordial Magnetic Fields with Back-Reaction of the Turbulent Medium