Effect of thermal fluctuations on homogeneous compressible turbulence

For more than a century, it has been widely believed that there is a clear gap between molecular motions at the microscopic level and turbulent fluctuations at the macroscopic level. However, recent studies have demonstrated that the thermal fluctuations resulted from molecular motions have nonnegligible effects on the dissipation range of turbulence. To further clarify the reviving debate on this topic, we employ the molecular-level direct simulation Monte Carlo (DSMC) method to simulate homogeneous turbulence with different turbulent Mach numbers, extending the previous studies by considering the effect of compressibility. Our results show that, for both one-dimensional (1D) stationary turbulence and two-dimensional (2D) decaying isotropic turbulence, the turbulent energy spectra are significantly changed due to thermal fluctuations below the spatial scale comparable to the turbulent dissipation length scale. The energy spectra caused by thermal fluctuations for different spatial dimensions d present different scaling laws of the wavenumber k as k^(d-1) . For 2D cases, we show that the effect of thermal fluctuations on the spectrum of compressible velocity component is greatly affected by the change of compressibility. The 2D spectra of density, temperature and pressure are also obtained, showing the same scaling law at large wavenumbers as found for the energy spectra. Moreover, it is found that the effects of thermal fluctuations on the thermodynamic spectra are the same as those on the spectra of compressible velocity component.