Fluctuating Hydrodynamics of Homogeneous Isotropic Compressible Turbulence

Using a fluctuating hydrodynamics description of fluids, we model the effects of molecular fluctuations on homogeneous, isotropic compressible turbulence in the nonlinear subsonic regime. We show that molecular fluctuations not only modify energy spectra at wavelengths larger than the Kolmogorov length scales in compressible turbulence, but also inhibit spatio-temporal intermittency across the dissipation range. Using large-scale direct numerical simulations of computational fluctuating hydrodynamics, we demonstrate that the extreme intermittency characteristic of turbulence models is replaced by nearly-Gaussian statistics in the dissipation range. Our results are in good agreement with recent and rediscovered theoretical predictions on the role of thermal noise in turbulence [1,2], as well as recent molecular gas dynamics simulations of decaying compressible turbulence [3]. Our results demonstrate that the compressible Navier-Stokes equations should be augmented with molecular fluctuations to accurately predict turbulence statistics across the dissipation range.

[1] J. Bell, A. Nonaka, A. Garcia, G. Eyink, J. Fluid Mech., 939, A12 (2022)

[2] D. Bandak, N. Goldenfeld, A. Mailybaev, G. Eyink, Phys. Rev. E, 105, 065113 (2022)

[3] R. McMullen, M. Krygier, J. Torczynski, M. Gallis, Phys. Rev. Lett., 128, 114501 (2022)