We show that spatio-temporal non-Markovianity of a Gaussian random synthetic velocity field is an essential property for modelling turbulent mixing. We demonstrate this using synthetically generated Gaussian incompressible velocity fields for passive scalar mixing. Including a separate velocity decorrelation time scale for each spatial scale (random sweeping) yields an essentially non-Markovian velocity field with a finite time memory decaying as ^-6 (for a decaying spectrum) instead of an exponential decay (Markovian), which is obtained by including a constant time scale for all spatial scales, irrespective of the filtering function. We characterise the Lagrangian mixing statistics of both the Markovian and the non-Markovian synthetic fields and compare them against a corresponding incompressible direct numerical simulation (DNS). We show that the average pair dispersion is well captured by the non-Markovian fields across the ballistic, inertial and diffusive regimes. We also study diffusive passive scalar mixing in the Schmidt number range Sc 1 using the DNS and the synthetic fields. Both the synthetic fields recover the -17/3 scalar spectrum for low Schmidt numbers and inertial subrange in kinetic energy spectra. However, the mean fluctuation gradient magnitudes are severely under predicted by the Markovian synthetic fields compared with the non-Markovian synthetic fields. Additionally, the fluctuation gradients parallel to the mean gradient exhibit smaller skewness when stirred by the Markovian synthetic field compared with the non-Markovian fields. Finally, we show that the non-Markovian synthetic fields perform better in decaying scalar gradient simulations initialised by a concentrated sphere with high passive scalar concentration. Throughout, we compare our results with companion three-dimensional DNS to show the necessity of non-Markovianity in synthetic fields to capture mixing dynamics.
Awasthi et al. (Thu,) studied this question.