How much Navier–Stokes dynamics is needed to capture turbulent mixing?

We study the mixing of passive scalars in a velocity field generated by selected-eddy simulations (SES), an approach where only a randomly selected subset of spectrally distributed modes obey Navier–Stokes dynamics. The Taylor Reynolds number varies from 140 to 400 and the Schmidt number ( $Sc$ ) varies from 0.25 to 1. By comparing the results with direct numerical simulations (DNS), we show that most statistics are captured with as low as $0.5\,\%$ of Navier–Stokes modes in the velocity field. This includes scalar gradients, spectra, structure functions and their departures from classical scaling due to intermittency. The results suggest that all modes need not be resolved to accurately capture turbulent mixing for $Sc\leqslant 1$ scalars.