Direct numerical simulations of compressible turbulence in a periodic box: Effect of isothermal assumptions on turbulence statistics

Direct numerical simulations of compressible nonisothermal turbulence in a periodic box with up to $40963$ grid points were conducted by varying Reynolds numbers and resolution levels. The results were compared with those of compressible isothermal turbulence by Sakurai and Ishihara [“Direct numerical simulations of compressible isothermal turbulence in a periodic box: Reynolds number and resolution-level dependence,” Phys. Rev. Fluids 8, 084606 (2023)] to study the effect of isothermal assumption on turbulence statistics. The turbulent Mach number and ratio of the dilatational to solenoidal root mean square velocities were fixed at approximately 0.3 and 0.4, respectively. A comparison under approximately equal flow conditions showed that the dilatational component of the energy spectra for the nonisothermal case exhibited approximately equal $k−3$ scaling at $kη>1$ as observed for the isothermal case and was consistently smaller in the wavenumber range $0.05<kη<0.6$ than that for the isothermal case, where $η$ is the Kolmogorov length. The dilatational energy is mainly dissipated around $kη≈0.3$⁠, the same wavenumbers as the solenoidal energy dissipation irrespective of the isothermal assumption. As the Reynolds number increased, the dilatational energy dissipation caused by shocklets around $kη≈2$ became larger, especially in the nonisothermal case. It was found that the isothermal assumption weakened the intermittency of the velocity divergence. No significant differences were observed in the normalized mean energy dissipation rates and pressure statistics. The local flow topology was also marginally affected by the isothermal assumption; however, the difference was significantly less than the changes owing to the different values of parameters such as the Reynolds number and Mach number.