To investigate the dynamics of the mantle's D″ layer, we explore numerical models of mantle convection which feature a dense basal boundary layer. We use a double-diffusive finite element convection scheme and vary thermal and chemical Rayleigh numbers and properties including viscosity, thermal conductivity, and internal heating. For isoviscous models with heating only from below, the thermal Rayleigh number (Ra) is set at either 106 or 107. The negative chemical buoyancy of a dense layer produces a stable boundary layer when the ratio of chemical to thermal buoyancy (the buoyancy number B) is around 1. For B=0.5 the layer is unstable, while B=0.6 may produce a layer which remains stable for long periods, depending on other factors (such as Rayleigh number, layer thickness, and thermal diffusivity of the layer). At high enough Ra, small-scale convection can occur within the layer. Using Ra=107, we look at changes in layer thickness from 100 to 300 km at two values of B (0.6 and 1). Convection within the layer takes place most easily when the layer has a greater initial thickness. For B=0.6, the layer is not always continuous along the lower boundary, so convection within the layer does not occur unless the initial thickness is fairly high (300 km). Increasing the thermal diffusivity of the layer (to simulate enrichment in metals) enhances heat conduction across the layer and can suppress internal convection within D″. Enhanced conduction also leads to higher plume temperatures. Including internal heating mainly increases the overall heat flow through the mantle, leading to higher surface heat flux. Finally, we examine models with temperature-dependent viscosity and pressure-dependent viscosity using Rayleigh numbers in the range of 107. Convection within the dense layer is enhanced by the relative reduction in viscosity. Our models exhibit only a modest decrease in viscosity (an order of magnitude) but illustrate how a dense, low-viscosity layer interacts with cold, viscous downwellings. ¿ 2000 American Geophysical Union