On the advection of sharp material interfaces in geodynamic problems: entrainment of the D layer

The Dʹʹ layer is a dense and chemically distinct layer at the base of the convecting mantle. Numerical modeling of the entrainment of this layer by mantle convection requires the solution of the advective transport equation without introducing numerical diffusion across sharp material boundaries. We use our improved second moment numerical method to solve the equation. The method conserves the amount of material and the first and second moments of material distribution in each control volume. We first consider two examples of isothermal Rayleigh-Taylor instability to illustrate the performance of our method by comparing our results with those of a number of field, tracer and marker chain methods. We show that the performance of our method in minimizing the numerical diffusion is better than the field methods and comparable to the tracer and marker chain methods. We then study the instability of the dense Dʹʹ layer and its interaction with the overlying mantle. A range of density contrast between the Dʹʹ layer and the mantle, layer thickness, and the Rayleigh number, Ra, is examined. We show that for higher values of these parameters, the amount of entrainment decreases and the layer remains stable over longer periods of time. For very thick Dʹʹ layers and high Ra values, internal convection can take place within the layer.