On the time irreversibility of compressible turbulence reflected by particles of various inertias

Abstract

Time irreversibility of compressible homogeneous isotropic turbulence (HIT) is investigated from a Lagrangian point of view and single-particle statistics. For this purpose, direct numerical simulation (DNS) is implemented for compressible HIT at Taylor-mircoscale Reynolds number Reλ∼100 and turbulent Mach number Mt up to 1.01, in which tracers and inertial particles in a wide Stokes number (St) range are instantaneously tracked with time. The statistics of instantaneous power of particles corroborates that the violation of detailed balance of turbulence in compressible HIT is much stronger than in incompressible HIT. It turns out that the third moment of dimensionless instantaneous power (Ir) of tracers scales as Mt4. A possible explanation based on Kolmogorov-like argument proves to be plausible due to the lacks of direct verification and generality for other moments of the power. A further analysis from an Eulerian point of view suggests that the underlying mechanism for time irreversibility of highly compressible turbulence is quite different from that for weakly compressible or incompressible turbulence. For inertial particles, the moments of instantaneous power are suggested to scale as St−2n/3 at relatively large St numbers, and be dependent only on Mach number or Reynolds number at the small-St number end, which are manifested by the present numerical data. It is further shown that the empirical Mt4 scaling of Ir also approximately applies to various inertial particles, but only at high Mt numbers due to the diminishing effect of compressibility to the low-Mach number end. The time irreversibility announced by the Lagrangian statistical properties of particles of different inertias is shown to be highly associated with their responses to the vortex and shocklet structures in compressible turbulence.