Coexistence of acoustic waves and turbulence in low Mach number compressible flows

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, modally equipartitioned compressible, and compressible wave. 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.