  The power spectrum of a homogeneous and isotropic stochastic variable,
characterized by a finite correlation length, does in general not vanish on
scales larger than the correlation scale. If the variable is a divergence free
vector field, we demonstrate that its power spectrum is blue on large scales.
Accounting for this fact, we compute the gravitational waves induced by an
incompressible turbulent fluid and by a causal magnetic field present in the
early universe. The gravitational wave power spectra show common features: they
are both blue on large scales, and peak at the correlation scale. However, the
magnetic field can be treated as a coherent source and it is active for a long
time. This results in a very effective conversion of magnetic energy in
gravitational wave energy at horizon crossing. Turbulence instead acts as a
source for gravitational waves over a time interval much shorter than a Hubble
time, and the conversion into gravitational wave energy is much less effective.
We also derive a strong constraint on the amplitude of a primordial magnetic
field when the correlation length is much smaller than the horizon.
