  An analytical model for three-dimensional incompressible turbulence was
recently introduced in the hydrodynamics community which, with only a few
parameters, shares many properties of experimental and numerical turbulence,
notably intermittency (non-Gaussianity), the energy cascade (skewness), and
vorticity alignment properties. In view of modeling astrophysical environments,
we introduce a manner to extend to compressible fluids the three-dimensional
turbulent velocity field model of Chevillard et al. (2010), as well as the
three 3D turbulent magnetic field models of Durrive et al. (2020), following
the same procedure based on the concept of multiplicative chaos. Our model
provides a complementary tool to numerical simulations, as it enables us to
generate very quickly fairly realistic velocity fields and magnetic fields, the
statistics of which are controllable with intuitive parameters. Therefore our
model will also provide a useful tool for observers in astrophysics. Finally,
maybe even more than the model itself, it is the very procedure that matters
the most: our model is modular, in the sense that it is constructed gradually,
with intuitive and physically motivated steps, so that it is prone to many
further improvements.
