  We study the gravitational wave (GW) signal sourced by primordial turbulence
that is assumed to be present at cosmological phase transitions like the
electroweak and quantum chromodynamics phase transitions. We consider various
models of primordial turbulence, such as those with and without helicity,
purely hydrodynamical turbulence induced by fluid motions, and
magnetohydrodynamic turbulence whose energy can be dominated either by kinetic
or magnetic energy, depending on the nature of the turbulence. We also study
circularly polarized GWs generated by parity violating sources such as helical
turbulence. Our ultimate goal is to determine the efficiency of GW production
through different classes of turbulence. We find that the GW energy and strain
tend to be large for acoustic or irrotational turbulence, even though its
tensor mode amplitude is relatively small at most wave numbers. Only at very
small wave numbers is the spectral tensor mode significant, which might explain
the efficient GW production in that case.
