Abstract
We present an extensive numerical study of the time irreversibility of the dynamics of heavy inertial particles in three-dimensional, statistically homogeneous, and isotropic turbulent flows. We show that the probability density function (PDF) of the increment, , of a particle's energy over a time scale is non-Gaussian, and skewed toward negative values. This implies that, on average, particles gain energy over a period of time that is longer than the duration over which they lose energy. We call this slow gain and fast loss. We find that the third moment of scales as for small values of . We show that the PDF of power-input is negatively skewed too; we use this skewness as a measure of the time irreversibility and we demonstrate that it increases sharply with the Stokes number for small ; this increase slows down at . Furthermore, we obtain the PDFs of and , the times over which has, respectively, positive or negative signs, i.e., the particle gains or loses energy. We obtain from these PDFs a direct and natural quantification of the slow gain and fast loss of the energy of the particles, because these PDFs possess exponential tails from which we infer the characteristic loss and gain times and , respectively, and we obtain for all the cases we have considered. Finally, we show that the fast loss of energy occurs with greater probability in the strain-dominated region than in the vortical one; in contrast, the slow gain in the energy of the particles is equally likely in vortical or strain-dominated regions of the flow.
- Received 21 November 2017
DOI:https://doi.org/10.1103/PhysRevE.97.033102
©2018 American Physical Society