We consider the time dependence of a hierarchy of scaled L
2m
-norms Dm,ω and Dm,θ
of the vorticity ω = ∇ × u and the density gradient ∇θ, where θ = log(ρ∗
/ρ∗
0
), in
a buoyancy-driven turbulent flow as simulated by Livescu & Ristorcelli (J. Fluid
Mech., vol. 591, 2007, pp. 43–71). Here, ρ
∗
(x, t) is the composition density of a
mixture of two incompressible miscible fluids with fluid densities ρ
∗
2 > ρ∗
1
, and ρ
∗
0
is a reference normalization density. Using data from the publicly available Johns
Hopkins turbulence database, we present evidence that the L
2
-spatial average of the
density gradient ∇θ can reach extremely large values at intermediate times, even
in flows with low Atwood number At = (ρ∗
2 − ρ
∗
1
)/(ρ∗
2 + ρ
∗
1
) = 0.05, implying that
very strong mixing of the density field at small scales can arise in buoyancy-driven
turbulence. This large growth raises the possibility that the density gradient ∇θ might
blow up in a finite time.