In this workshop we studied a specific type of hydrodynamics instability, the Rayleigh Benard convection phenomena. With some initial conditions, the coupling between fluid dynamics and heat transfert  leads to the development of convection rolls in the flow.

           We chose to study a specific application of this phenomena: convection in the earth mantle.  The magma is a very viscous fluid with a very slow motion, interacting with the tectonics plates moving on it: scientists  advanced two different hypothesis to describe what happens in the mantle, and we used Fluent to try to simulate them with a very simple model.

           The phase change at  670 km is the key-parameter in the description of convection in the mantle:

• The first model advanced by scientists is a 1-layer model where there would be just one layer of convection rolls (image A).

• The second model is a 2-layers model: convection is organized in 2 layers, the upper mantle layer, 700 km thick, and the lower mantle layer, 2200 km thick, would both present convection rolls. This 2-layers model is compatible  with the changes in the mantle rheology which occur at around 700 km depth (image C).

• A third model is an intermediate model: the upper mantle, cooler, stays on the discontinuity, but manages to cross it at some locations. This could explain why in subduction areas tectonic plates seem to go deeper than 670 km.

            We used Fluent to try to simulate the convection in the mantle, we made the hypothesis that the viscosity gradient was playing the main role in the mantle convection mecanism: therefore we chose to initialize the phenomona with a viscosity gradient between the two mantle layers.
 

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