Energy spectra in compressible turbulence: regimes and scaling*

The energy spectrum in compressible turbulence is studied systematically using a large direct numerical simulation (DNS) database of forced isotropic compressible turbulence with solenoidal and dilatational forcing. The database comprises a wide range of compressibility conditions. We demonstrate that traditional parameters (Reynolds and turbulent Mach numbers) fail to characterize the complex behavior manifested by the dilatational part of the energy  spectrum. We develop a new asymptotic analysis based on two compressibility parameters, M_t and δ the ratio of dilatational to solenoidal root-mean-square velocity.  The scaling laws predicted by the asymptotic analysis agree well with the DNS data. Analysis of dominant terms stemming from the asymptotic  expansion show a number of different regimes (based on M_t and δ) of compressible turbulence. They include cascade and non-cascade regimes,  pseudo-sound, as well as different equipartition regimes. Our analysis further allows us to identify specific spectral behavior in each of these regimes, which are compared to DNS data. All the results are discussed in the context of the δ-M_t plane to reconcile disagreements in the literature.