Geophysical Fluid Dynamics, **Machine** VP

Research School of Earth Sciences

**Mantle Plumes**

Convection is the way in which heat and material are transferred from the deep Earth to the near surface. In this project, large-scale numerical simulations of convection are used to study various aspects of convection in the Earth's mantle.

**What are the basic questions addressed?**

One current project is concerned with how the core temperature of rising hot limbs (two-dimensional `sheets' or axisymmetric `plumes') in convection cells is influenced by the geometry of the cells and the vigour of convection. A second project studies the amount of melting present in a hot, axisymmetric blob as it approaches the surface of the Earth.

**What are the results to date and the future of the work?**

The first project used the versatile finite-element code PDEprotran to carry out simulations of convection in a cartesian box, an axisymmetric cylinder and an axisymmetric spherical shell. Temperature loss in the sheets and plumes was compared to simple mathematical models. The work has been completed and a paper is being written. It was found that the decrease in core temperatures for both sheets and plumes can be adequately described by simple models of one-dimensional diffusion of heat, once the convection cells are properly characterized in terms of velocities and aspect ratios. For sheets over a reasonable range of cell shapes, temperature loss is large (50-90%) and controlled by the aspect ratio and the ratio of horizontal and vertical velocities in the boundary layers. It is independent of convective vigour. For plumes, temperature loss is much less (2-30% for vigorous convection) and is controlled by aspect ratio, the velocity of the fluid feeding into the plume, and convective vigour. It decreases significantly as convection becomes more vigorous.

For the second project, CONMG, a multigrid finite-difference code developed by Dr Geoff Davies of this department, is being used. Equations which account for the release of latent heat for a simplified pressure-temperature melting relation have been added to the code, and some preliminary results have been obtained. These results indicate a relatively small amount of melting occurs in a limited area. To match geological findings, and allow plume material to get closer to the surface where it will melt more, it may be necessary to introduce a non-linear rheology to the code. However, the effects of different melting relations will be investigated first.

**What computational techniques are used and why is a supercomputer
required?**

The two codes used in this project both require the speed and memory resources of a supercomputer if results relevant to the Earth are to be obtained. PDEprotran is a general and versatile finite-element code distributed by IMSL. CONMG is a multigrid finite-difference code developed by Dr Geoff Davies of the Research School of Earth Sciences.