We report direct numerical simulation (DNS) and large-eddy simulation (LES) of
statistically stationary buoyancy-driven turbulent mixing of an active scalar. We use
an adaptation of the fringe-region technique, which continually supplies the flow with
unmixed fluids at two opposite faces of a triply periodic domain in the presence
of gravity, effectively maintaining an unstably stratified, but statistically stationary
flow. We also develop a new method to solve the governing equations, based on
the Helmholtz–Hodge decomposition, that guarantees discrete mass conservation
regardless of iteration errors. Whilst some statistics were found to be sensitive to the
computational box size, we show, from inner-scaled planar spectra, that the small
scales exhibit similarity independent of Reynolds number, density ratio and aspect
ratio. We also perform LES of the present flow using the stretched-vortex subgridscale
(SGS) model. The utility of an SGS scalar flux closure for passive scalars is
demonstrated in the present active-scalar, stably stratified flow setting. The multi-scale
character of the stretched-vortex SGS model is shown to enable extension of some
second-order statistics to subgrid scales. Comparisons with DNS velocity spectra
and velocity-density cospectra show that both the resolved-scale and SGS-extended
components of the LES spectra accurately capture important features of the DNS
spectra, including small-scale anisotropy and the shape of the viscous roll-off