  In this work, direct numerical simulations of the compressible fluid
equations in turbulent regimes are performed. The behavior of the flow is
either dominated by purely turbulent phenomena or by the generation of sound
waves in it. Previous studies suggest that three different types of turbulence
may happen at the low Mach number limit in polytropic flows: Nearly
incompressible (NI), modally equipartitioned compressible (MEC) and
compressible wave (CW). The distinction between these types of turbulence is
investigated here applying different kinds of forcing. Scaling of density
fluctuations with Mach number, comparison of the ratio of transverse velocity
fluctuations to longitudinal fluctuations and spectral decomposition of
fluctuations are used to distinguish the nature of these solutions. From the
study of the spatio-temporal spectra and correlation times we quantify the
contribution of the waves to the total energy of the system. Also, in the
dynamics of a compressible flow, three associated correlation times are
considered: the non-linear time of local interaction between scales, the
sweeping time or non-local time of large scales on small scales, and the time
associated with acoustic waves (sound). We observed that different correlation
times dominate depending on the wave number (k), the Mach number and the type
of forcing.
