Scalar mixing in non-Markovian homogeneous isotropic synthetic turbulence

Abstract

We show that non-Markovianity of the velocity field is an essential property of turbulent mixing. We demonstrate this via passive scalar mixing by synthetically generated stochastic velocity fields. 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 -5 (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 characterize the Lagrangian mixing statistics of both the Markovian and non-Markovian synthetic fields and compare them against a corresponding incompressible direct numerical simulation (DNS). We also study diffusive passive scalar mixing in the Schmidt number range Sc<1 using the DNS and the synthetic fields. While both the synthetic fields recover the -17/3 scalar spectrum for low Schmidt numbers, the mean gradients in a decaying simulation, as well as the production and dissipation of scalar variance in a statistically stationary simulation, are severely underpredicted by the Markovian fields compared to the non-Markovian fields. Throughout, we compare our results with companion 3D DNS to show the necessity of non-Markovianity in synthetic fields to capture mixing dynamics.