Effects of multitemperature nonequilibrium on compressible homogeneous turbulence

We study the effects of the rotational-translational energy exchange on the compressible decaying homogeneous isotropic turbulence (DHIT) in three dimensions through direct numerical simulations. We use the gas-kinetic scheme coupled with multitemperature nonequilibrium based on the Jeans-Landau-Teller model. We investigate the effects of the relaxation time of rotational temperature, Z(R), and the initial ratio of the rotational and translational temperatures, T-R0/T-L0, on the dynamics of various turbulence statistics including the kinetic energy K(t), the dissipation rate epsilon(t), the energy spectrum E(k,t), the root mean square of the velocity divergence theta(')(t), the skewness S-u(t) and the flatness F-u(t) of the velocity derivatives, and the probability distribution functions of the local Mach number Ma and the shocklet strength chi. The larger the Z(R) is, the faster the compressibility decays after an initial time. Similarly, with a fixed T-L0, the higher the initial energy ratio T-R0/T-L0, the weaker is the compressibility in the flow. It is also observed that the effect of T-R0/T-L0 is strong in all times in the decay, while the effect of Z(R) is severe only in the later times passing through the stage with strong nonlinearity. We also observe that the multitemperature model does not affect the self-similarities obeyed by the probability distribution functions of Ma and chi, which appear to be a robust feature of the compressible DHIT.