**Principal Investigator**
Alison Leitch **Project** r01

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 recent project was concerned with how the core temperature and width of rising or sinking 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 blob as it approaches the surface of the Earth.

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

In the first project, the versatile finite-element code PDEprotran was used to carry out simulations of convection in a cartesian box, an axisymmetric cylinder and an axisymmetric spherical shell. Temperature loss and thicknesses of the sheets and plumes was compared to simple mathematical models. 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 same "catchment area" of fluid feeding into the upward flow, plumes are 2-3 times wider than sheets. The work has been completed and a paper submitted.

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 pressure-temperature melting relation appropriate to the Earth, and calculations of the volume of melting have been added to the code by the PI. A project currently underway is studying the amount and duration of melting produced when a continent breaks apart ("rifts") forming a new ocean basin, when the rift is underlain by a blob of hot material - the head of a mantle plume. Off the east coast of the USA is a region of anomalously thick ocean crust: we are studying the possibility that the thicker crust is due to excess melting in the plume.

Future work will study melting in a plume of more realistic shape and in axisymmetric geometry. This may involve grid refinement in the code, since melting occurs in a very limited area. Work on grid refinement is in progress. All currently envisaged work will use the code CONMG.

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

The code used in this project requires the speed and memory resources of a supercomputer if results relevant to the Earth are to be obtained. CONMG is a multigrid finite-difference code developed by Dr Geoff Davies of the Research School of Earth Sciences. This code can run on a workstation, but to study melting problems (the aim of this project) very high resolution is needed, involving 40-160MB of core memory. With the VP, results can be obtained in 10-30 minutes that would take hours or days on a workstation.

**Publications**

*Centerline Temperature of Mantle Plumes in Various
Geometries: Incompressible Flow,* A.M.
Leitch, V. Steinbach and D.A. Yuen J. Geophys. Res submitted.