  In 1D evolution models of gas giant planets, an outer convection zone
advances into the interior as the surface cools, and multiple convective layers
form beneath that convective front. To study layer formation below an outer
convection zone in a similar scenario, we investigate the evolution of a
stably-stratified fluid with a linear composition gradient that is constantly
being cooled from above. We use the Boussinesq approximation in a series of 2D
simulations at low and high Prandtl numbers ($\mathrm{Pr} = 0.5$ and 7),
initialized with constant temperature everywhere, and cooled at different
rates. We find that multiple convective layers form at $\mathrm{Pr} = 7$, {as
the result of an instability in the} diffusive thermal boundary layer below the
outer convection zone. At low Pr, layers do not form because the temperature
gradient within the boundary layer is much smaller than at large Pr and,
consequently, is not large enough to overcome the stabilizing effect of the
composition gradient. For the stratification used in this study, on the
long-term the composition gradient is an ineffective barrier against the
propagation of the outer convection zone and the entire fluid becomes
fully-mixed, whether layers form or not. Our results challenge 1D evolutionary
models of gas giant planets, which predict that layers are long-lived and that
the outer convective envelope stops advancing inwards. We discuss what is
needed for future work to build more realistic models.
