Compressible hydrodynamic turbulence is studied under the assumption of a polytropic closure. Following Kolmogorov, we derive an exact relation for some two-point correlation functions in the asymptotic limit of a high Reynolds number. The inertial range is characterized by: (i) a flux term implying in particular the enthalpy; and (ii) a purely compressible term may impose another scaling depending on the polytropic index. In both cases, it is shown that the fluctuating sound speed is a key ingredient for understanding polytropic compressible turbulence.
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Banerjee et al. (2014) studied this question.
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