Scaling of energy spectra in weakly compressible turbulence

We find an asymptotic expression for the characteristic timescales of decorrelation processes in weakly compressible and isothermal turbulence. This result is used in the Eddy-Damped Quasi-Normal Markovian equation to derive the scalings of compressible energy spectra: (1) if the acoustic waves are dominant, the compressible energy spectra exhibit scaling; (2) if local eddy straining is dominant, the compressible energy spectra are scaled as . Meanwhile, the energy spectra of incompressible components display the same scaling of as those in incompressible turbulence. The direct numerical simulations of weakly compressible turbulence are used to examine the scaling.