Small-scale resolving simulations of the turbulent mixing in confined planar jets using one-dimensional turbulence

Abstract

Small-scale effects of turbulent mixing are numerically investigated by applying the map-based, stochastic, one-dimensional turbulence (ODT) model to confined planar jets. The model validation is carried out for the momentum transport by comparing ODT results to available reference data for the bulk Reynolds numbers $Re=20\,000$ and $40\,000$. Various pointwise statistical quantities are computed and compared to the available reference data. We show that these quantities can be captured well, or at least to a reasonable extent, by the stand-alone model formulation and for fixed model parameters. Only the root-mean-square velocity fluctuations remain systematically underestimated in the ODT results (by an approximate factor of $1.5$). Afterwards, the turbulent transport of a passive scalar is addressed for the Schmidt numbers $Sc=1$ and $1250$. For the high Schmidt number and in contrast to the velocity fluctuations, it is shown that the scalar fluctuation variance is up to ten times larger in the ODT simulations resolving the Batchelor scale. The fluctuation variance is notably smaller for the lower Schmidt number, but exhibits better agreement with the references at a nominally higher Schmidt number. We suggest that this is due to implicit filtering in the references, which barely resolve the Kolmogorov scale. ODT turbulence spectra support this interpretation since a Batchelor-like scalar turbulence spectrum is only observed for the higher Schmidt number. With the aid of these spectra and the fluctuation statistics we conclude that implicit filtering has a similar effect as a reduction of the Schmidt number.