Gravitational Waves produced by Compressible MHD Turbulence from
  Cosmological Phase Transitions
  We calculate the gravitational wave spectrum produced by magneto-hydrodynamic
turbulence in a first order phase transitions. We focus in particular on the
role of decorrelation of incompressible (solenoidal) homogeneous isotropic
turbulence, which is dominated by the sweeping effect. The sweeping effect
describes that turbulent decorrelation is primarily due to the small scale
eddies being swept with by large scale eddies in a stochastic manner. This
effect reduces the gravitational wave signal produced by incompressible MHD
turbulence by around an order of magnitude compared to previous studies.
Additionally, we find a more complicated dependence for the spectral shape of
the gravitational wave spectrum on the energy density sourced by solenoidal
modes (magnetic and kinetic). The high frequency tail follows either a
$k^{-5/3}$ or a $k^{-8/3}$ power law for large and small solenoidal turbulence
density parameter, respectively. Further, magnetic helicity tends to increase
the gravitational wave energy at low frequencies. Moreover, we show how
solenoidal modes might impact the gravitational wave spectrum from dilatational
modes e.g. sound waves. We find that solenoidal modes greatly affect the shape
of the gravitational wave spectrum due to the sweeping effect on the
dilatational modes. For a high velocity flow, one expects a $k^{-2}$ high
frequency tail, due to sweeping. In contrast, for a low velocity flow and a
sound wave dominated flow, we expect a $k^{-3}$ high frequency tail. If neither
of these limiting cases is realized, the gravitational wave spectrum may be a
broken power law with index between -2 and -3, extending up to the frequency at
which the source is damped by viscous dissipation.
