Filter-width and Atwood number effects in filtered homogeneous variable density turbulence

We investigate Atwood number ($A)$ and filter width ($w)$ dependence in filtered DNS of buoyancy driven homogeneous variable density turbulence, where density differences affect mixing and turbulence, and we discuss implications for modeling. We show that statistics and budgets of filtered fields transition smoothly between DNS and RANS fields and budgets, and we discuss these transitions in the context of flow length scales. At small $w$, filtered fields tend to DNS fields and the large-scale flow kinetic energy ($k_{l})$ budget tends to the total kinetic energy ($k_{t})$ budget; at large $w$, filtered fields approach RANS fields and $k_{l}$ approaches the mean kinetic energy ($k_{m})$ budget. At intermediate $w$, the $k_{l}$ budget has dissipation and pressure-dilatation work terms from the $k_{t}$ budget, a mean pressure gradient term from the $k_{m}$ budget, a production term from both the $k_{t}$ and $k_{m}$ budgets, and work by residual stresses against the filtered shear $e_{s}$, which tends to zero at both limits. Work by mean pressure gradients and by $e_{s}$ exhibit density dependent back-scatter: at high $A$, $e_{s}$ back-scatter occurs mainly in light fluid. Statistics of filtered fields, normalized by their RANS counterparts, smoothly and monotonically vary between 0 and 1 as $w$ varies from d$x$ to domain size, and the dependence on $w$ is different for different quantities.