In 1970, two independent studies (by Wunsch and Phillips) of the behaviour of a linear density-stratified fluid in a closed container demonstrated a flow can be generated \emph{simply due to the container having a sloping boundary surface}. This remarkable motion is generated as a result of the curvature of the lines of constant density near any sloping surface, which in turn enables a zero normal-flux condition on the density to be satisfied along that boundary. When the Rayleigh number is large (or equivalently Wunsch's parameter $R$ is small) this motion is concentrated in the near vicinity of the sloping surface, in a thin `buoyancy layer' that has many similarities to an Ekman layer in a rotating fluid. A number of studies have since considered the consequences of this type of `diffusively-driven' flow, including in the deep ocean and with turbulent effects included. At the 2008 ANZIAM Conference I outlined a \emph{steady linear} theory for the broader-scale mass recirculation in a closed container and demonstrated that, unlike in previous studies, it is possible for the buoyancy layer to entrain fluid from that recirculation [Journal of Fluid Mechanics, 2008, 606:433--443]. In this talk that work will be extended to the unsteady and nonlinear regimes of the problem and some of the similarities to and differences from the linear case will be described. Simple and elegant analytical solutions in the limit as $R \to 0$ still exist in some situations, and they will be compared with both numerical simulations for small values of $R$ and published experimental results.