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We study the formation and evolution of a convective layer when astably-stratified fluid with a composition gradient is cooled from above. Weperform a series of 2D simulations using the Bousinessq approximation withPrandtl number ranging from Pr = 0.1 to 7, extending previous work on saltywater to low Pr. We show that the evolution of the convection zone iswell-described by an entrainment prescription in which a fixed fraction of thekinetic energy of convective motions is used to mix fluid at the interface withthe stable layer. We measure the entrainment efficiency and find that it growswith decreasing Prandtl number or increased applied heat flux. The kineticenergy flux that determines the entrainment rate is a small fraction of thetotal convective luminosity. In this time-dependent situation, the densityratio at the interface is driven to a narrow range that depends on the value ofPr, and with low enough values that advection dominates the interfacialtransport. We characterize the interfacial flux ratio and how it depends on theinterface stability. We present an analytic model that accounts for the growthof the convective layer with two parameters, the entrainment efficiency and theinterfacial heat transport, both of which can be measure from the simulations.

Penetration of a cooling convective layer into a stably-stratified composition gradient: entrainment at low Prandtl number