  It is commonly accepted that the breakup criteria of drops or bubbles in
turbulence is governed by surface tension and inertia. However, also
{\it{buoyancy}} can play an important role at breakup. In order to better
understand this role, here we numerically study Rayleigh-B\'enard convection
for two immiscible fluid layers, in order to identify the effects of buoyancy
on interface breakup. We explore the parameter space spanned by the Weber
number $5\leq We \leq 5000$ (the ratio of inertia to surface tension) and the
density ratio between the two fluids $0.001 \leq \Lambda \leq 1$, at fixed
Rayleigh number $Ra=10^8$ and Prandtl number $Pr=1$. At low $We$, the interface
undulates due to plumes. When $We$ is larger than a critical value, the
interface eventually breaks up. Depending on $\Lambda$, two breakup types are
observed: The first type occurs at small $\Lambda \ll 1$ (e.g. air-water
systems) when local filament thicknesses exceed the Hinze length scale. The
second, strikingly different, type occurs at large $\Lambda$ with roughly $0.5
< \Lambda \le 1$ (e.g. oil-water systems): The layers undergo a periodic
overturning caused by buoyancy overwhelming surface tension. For both types the
breakup criteria can be derived from force balance arguments and show good
agreement with the numerical results.
