The mixing of a passive scalar field by turbulence that is generated by buoyancy forces acting on an initial random density field is considered. Various asymptotic similarity states of the passive scalar field with and without a uniform mean passive scalar gradient are determined by dimensional arguments based on exact- or near-invariants of the density and passive scalar fields. The results of large-eddy numerical simulations are shown to support the derived scaling laws. The large-eddy simulations also demonstrate the different mixing properties of an active and passive scalar field.
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