Effects of thermal non-equilibrium and molecular fluctuations on compressible decaying isotropic turbulence

This study employs the direct simulation Monte Carlo method to investigate two-dimensional compressible decaying isotropic turbulence under high Mach number conditions, focusing on the effects of thermal non-equilibrium (TNE) and molecular thermal fluctuations. Simulations are performed for low-temperature cases involving rotational non-equilibrium, followed by high-temperature cases emphasizing vibrational non-equilibrium. The results demonstrate that the initial TNE state significantly impacts turbulence compressibility. Specifically, for initially rotationally hot cases, elevated translational temperatures strongly suppress turbulence compressibility, resulting in a slower decay of turbulent kinetic energy. These findings are also applicable to initially vibrationally hot cases, but the influence of TNE diminishes as the vibrational relaxation number Zvib increases. Moreover, increasing Zvib leads to a significant lag of vibrational temperature fluctuations relative to translational and rotational temperature fluctuations. Analysis of the turbulent energy and temperature spectra reveals that molecular thermal fluctuations dominate at length scales (i.e., crossover length scales) comparable to the turbulent dissipation length scale, causing the spectra to increase linearly with the wavenumber. For cases with initially rotationally or vibrationally hot conditions, the suppression of compressibility leads to a significant increase in the crossover length scale.