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In this work, direct numerical simulations of the compressible fluidequations in turbulent regimes are performed. The behavior of the flow iseither dominated by purely turbulent phenomena or by the generation of soundwaves in it. Previous studies suggest that three different types of turbulencemay happen at the low Mach number limit in polytropic flows: Nearlyincompressible (NI), modally equipartitioned compressible (MEC) andcompressible wave (CW). The distinction between these types of turbulence isinvestigated here applying different kinds of forcing. Scaling of densityfluctuations with Mach number, comparison of the ratio of transverse velocityfluctuations to longitudinal fluctuations and spectral decomposition offluctuations are used to distinguish the nature of these solutions. From thestudy of the spatio-temporal spectra and correlation times we quantify thecontribution of the waves to the total energy of the system. Also, in thedynamics of a compressible flow, three associated correlation times areconsidered: the non-linear time of local interaction between scales, thesweeping time or non-local time of large scales on small scales, and the timeassociated with acoustic waves (sound). We observed that different correlationtimes dominate depending on the wave number (k), the Mach number and the typeof forcing.

Turbulence and acoustic waves in compressible flows