Scalar mixing in homogeneous isotropic turbulence: A numerical study

The understanding of the mechanics of turbulent dispersion is of primary importance in estimating the effects of mixing processes involved in a variety of events playing a significant role in our daily life. This motivates research on the characterization of statistics and the complex temporal evolution of passive scalars in turbulent flows. A key aspect of these studies is the modeling of the probability density function (PDF) of the passive scalar concentration and the identification of its link with the mixing properties. In order to investigate the dynamics of passive scalars as observed in nature and in laboratory experiments, we perform here direct numerical simulations of a passive tracer injected in the stationary phase of homogeneous isotropic turbulence flows in a setup mimicking the evolution of a fluid volume in the reference frame of the mean flow. In particular, we show how the gamma distribution proves to be a suitable model for the PDF of the passive scalar concentration and its temporal evolution in a turbulent flow throughout the different phases of the mixing process. Then, assuming a gamma distribution, we develop a simple mixing model by which we can estimate a mixing timescale, which regulates the decay rate of the intensity of the concentration fluctuations.