  Hydrodynamic and magnetohydrodynamic turbulence in the early Universe can
drive gravitational waves (GWs) and imprint their spectrum onto that of GWs,
which might still be observable today. We study the production of the GW
background from freely decaying magnetohydrodynamic turbulence from helical and
nonhelical initial magnetic fields. To understand the produced GW spectra, we
develop a simple model on the basis of the evolution of the magnetic stress
tensor. We find that the GW spectra obtained in this model reproduce those
obtained in numerical simulations if we consider the detailed time evolution of
the low-frequency tail of the stress spectrum from numerical simulations. We
also show that the shapes of the produced GW frequency spectra are different
for helical and nonhelical cases for the same initial magnetic energy spectra.
Such differences can help distinguish helical and nonhelical initial magnetic
fields from a polarized background of GWs -- especially when the expected
circular polarization cannot be detected directly.
