Effect of thermal fluctuations on homogeneous compressible turbulence

Abstract

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 $${{k}^{(d-1)}}$$ 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.

Effect of thermal fluctuations on spectra and predictability in compressible decaying isotropic turbulence

“…3.2. Unified stochastic particle method So far, the DSMC method (Bird 1994) is still the most commonly used molecular method for simulating rarefied gas flows, and it has recently been employed to investigate the effect of thermal fluctuations on turbulence (McMullen et al 2022b(McMullen et al , 2023Ma et al 2023). A typical DSMC simulation tracks an appropriate number of 'particles' (simulated molecules) in the computational domain.…”

“…Therefore, it can be concluded that, for gases in equilibrium, the 2-D energy spectrum grows linearly with the wavenumber k (Ma et al 2023), while the 3-D energy spectrum grows quadratically with k (Bandak et al 2022;Bell et al 2022;McMullen et al 2022b).…”

“…In recent years, the DSMC method has been extensively employed to simulate compressible turbulent gas flows (Gallis et al 2017(Gallis et al , 2018(Gallis et al , 2021McMullen et al 2022a,b;Ma et al 2023;McMullen, Torczynski & Gallis 2023), with several studies focusing on the effect of thermal fluctuations on turbulence statistics. McMullen et al (2022bMcMullen et al ( , 2023 employed the DSMC method to simulate the three-dimensional (3-D) Taylor-Green vortex flow, revealing significant influences of thermal fluctuations on both the turbulent energy spectra and velocity structure functions at dissipation length scales.…”

“…McMullen et al (2022bMcMullen et al ( , 2023 employed the DSMC method to simulate the three-dimensional (3-D) Taylor-Green vortex flow, revealing significant influences of thermal fluctuations on both the turbulent energy spectra and velocity structure functions at dissipation length scales. Our recent work (Ma et al 2023) employed DSMC to simulate the two-dimensional (2-D) decaying isotropic turbulence, indicating that thermal fluctuations impacted both energy spectra and thermodynamic spectra in the dissipation range. By applying the Helmholtz decomposition (Samtaney, Pullin & Kosović 2001;Wang et al 2012) to the 2-D velocity field, the effects of thermal fluctuations on the solenoidal and compressible velocity components were studied separately under different M t conditions (Ma et al 2023).…”

“…Our recent work (Ma et al 2023) employed DSMC to simulate the two-dimensional (2-D) decaying isotropic turbulence, indicating that thermal fluctuations impacted both energy spectra and thermodynamic spectra in the dissipation range. By applying the Helmholtz decomposition (Samtaney, Pullin & Kosović 2001;Wang et al 2012) to the 2-D velocity field, the effects of thermal fluctuations on the solenoidal and compressible velocity components were studied separately under different M t conditions (Ma et al 2023).…”