A novel forcing technique to simulate turbulent mixing in a decaying scalar field

To realize the full potential of Direct Numerical Simulation in turbulent mixing studies, it is necessary to develop numerical schemes capable of sustaining the flow physics of turbulent scalar quantities. In this work, a new scalar field forcing technique, termed "linear scalar forcing," is presented and evaluated for passive scalars. It is compared to both the well-known mean scalar gradient forcing technique and a low waveshell spectral forcing technique. The proposed forcing is designed to capture the physics of one-time scalar variance injection and the subsequent self-similar turbulent scalar field decay, whereas the mean scalar gradient forcing and low waveshell forcing techniques are representative of continuous scalar variance injection. The linear scalar forcing technique is examined over a range of Schmidt numbers, and the behavior of the proposed scalar forcing is analyzed using single and two-point statistics. The proposed scalar forcing technique is found to be perfectly isotropic, preserving accepted scalar field statistics (fluxes) and distributions (scalar quantity, dissipation rate). Additionally, it is found that the spectra resulting from the three scalar forcing techniques are comparable for unity Schmidt number conditions, but differences manifest at high Schmidt numbers. These disparities are reminiscent of those reported between scaling arguments suggested by theoretical predictions and experimental results for the viscous-convective subrange.