  We perform numerical simulations of gravitational waves (GWs) induced by
hydrodynamic and hydromagnetic turbulent sources that might have been present
at cosmological quantum chromodynamic (QCD) phase transitions. For turbulent
energies of about 4% of the radiation energy density, the typical scale of such
motions may have been a sizable fraction of the Hubble scale at that time. The
resulting GWs are found to have an energy fraction of about $10^{-9}$ of the
critical energy density in the nHz range today and may already have been
observed by the NANOGrav collaboration. This is further made possible by our
findings of shallower spectra proportional to the square root of the frequency
for nonhelical hydromagnetic turbulence. This implies more power at low
frequencies than for the steeper spectra previously anticipated. The behavior
toward higher frequencies depends strongly on the nature of the turbulence. For
vortical hydrodynamic and hydromagnetic turbulence, there is a sharp drop of
spectral GW energy by up to five orders of magnitude in the presence of
helicity, and somewhat less in the absence of helicity. For acoustic
hydrodynamic turbulence, the sharp drop is replaced by a power law decay,
albeit with a rather steep slope. Our study supports earlier findings of a
quadratic scaling of the GW energy with the magnetic energy of the turbulence
and inverse quadratic scaling with the peak frequency, which leads to larger GW
energies under QCD conditions.
