  The solar wind is a magnetized and turbulent plasma. Its turbulence is often
dominated by Alfv\'enic fluctuations and often deemed as nearly incompressible
far away from the Sun, as shown by in-situ measurements near 1AU. However, for
solar wind closer to the Sun, the plasma $\beta$ decreases (often lower than
unity) while the turbulent Mach number $M_t$ increases (can approach unity,
e.g., transonic fluctuations). These conditions could produce significantly
more compressible effects, characterized by enhanced density fluctuations, as
seen by several space missions. In this paper, a series of 3D MHD simulations
of turbulence are carried out to understand the properties of compressible
turbulence, particularly the generation of density fluctuations. We find that,
over a broad range of parameter space in plasma $\beta$, cross helicity and
polytropic index, the turbulent density fluctuations scale linearly as a
function of $M_t$, with the scaling coefficients showing weak dependence on
parameters. Furthermore, through detailed spatio-temporal analysis, we show
that the density fluctuations are dominated by low-frequency nonlinear
structures, rather than compressible MHD eigen-waves. These results could be
important for understanding how compressible turbulence contributes to solar
wind heating near the Sun.
