We have tested the ability of driven turbulence to generate magnetic field
structure from a weak uniform held using three-dimensional numerical simula
tions of incompressible turbulence. We used a pseudospectral code with a nu
merical resolution of up to 144(3) collocation points. We find that the mag
netic fields are amplified through held line stretching at a rate proportio
nal to the difference between the velocity and the magnetic field strength
times a constant. Equipartition between the kinetic and magnetic energy den
sities occurs at a scale somewhat smaller than the kinetic energy peak. Abo
ve the equipartition scale the velocity structure is, as expected, nearly i
sotropic. The magnetic held structure at these scales is uncertain, but the
field correlation function is very weak. At the equipartition scale the ma
gnetic fields show only a moderate degree of anisotropy, so the typical rad
ius of curvature of held lines is comparable to the typical perpendicular s
cale for field reversal. In other words, there are few held reversals withi
n eddies at the equipartition scale and no fine-grained series of reversals
at smaller scales. At scales below the equipartition scale, both velocity
and magnetic structures are anisotropic; the eddies are stretched along the
local magnetic field lines, and the magnetic energy dominates the kinetic
energy on the same scale by a factor that increases at higher wavenumbers.
We do not show a scale-free inertial range, but the power spectra are a fun
ction of resolution and/or the imposed viscosity and resistivity. Our resul
ts are consistent with the emergence of a scale-free inertial range at high
er Reynolds numbers.