Entrainment of a dense layer by thermal plumes

The large mismatch between Earthʹs heat flux and that which would be produced in a uniform mantle with the composition of the mid-ocean ridge basalt source region, and several recent seismic models, suggest that the bottom part of the mantle may form a compositionally distinct layer. The long-term stability of such a dense but hot abyssal layer may hinge on the rate of entrainment of the dense material by upwelling thermal plumes that would originate from the thermal boundary layer at the compositional boundary. We have formulated high-resolution numerical models to examine the efficiency of such an entrainment. To isolate the physics of entrainment, thermal buoyancy forces that drive the flow and entrain the dense material are prescribed in both space and time in axisymmetric finite-element models with an isoviscous structure. Our models employ a marker chain method to track the evolution of the material interface. Thermal plumes entrain the dense material, forming a concentric annular structure, with a hot thermal plume surrounding an inner cylinder of dense material. The entrainment rate is controlled by two parameters: the radius of the thermal plume, rT, and the ratio of compositional to thermal buoyancy, Rabt. The smaller rT is or the larger Rabt, the smaller the entrainment rate will be, as expected. As Rabt increases, the radius of the entrained compositional plume decreases, but the vertical velocity of the compositional plume also increases. We found that the entrainment rate scales as Ra-2.48btr3.80T, while the radius of the entrained compositional plume scales as Ra-1.43btr1.24T. For a mantle viscosity of 1021 Pas, thermal plumes with rT~ 100 km and temperature 600 K hotter than the ambient mantle, and with horizontal spacings that are approximately the same as the mantle thickness, and for a denser layer with a thickness of 1000 km and net negative buoyancy of approximately 1 per cent, more than 90 per cent of the dense material can survive for 4.5 Gyr.