rayleigh

Partie 2:Convection in the mantle

Structure of the Earth:

The structure of the earth is divided in three main parts:
.The first one is the external envelop, about 10 km deep, called the crust
.Then comes the mantle, where the structure is warmer and less viscous, about 2900 km deep
.Finally, the kern, which diameter is about 7000 km.

This division is superposed with an other one that distinguishes the lithosphere about a few hundred kilometers, made of uge rigid slabs that move at the surface of the earth.
This lithosphere, including the crust and the upper mantle, rigid, lays on the asthenosphere where the mantle becomes smoother on several hundred kilometers and where the convection movements develop.

Slab tectonic:

The movements of convection in the mantle are directly linked to the slab tectonic.
The slabs are in constant movement and their speed is about a few centimeters per year.
Oceans are the results of their divergence, and mountains of their collisions.

Oceanic ridges can create gaps of about 15 cm per year, from those gaps merges the basalts that regenerate the earth's crust.

When the slabs get closer , one goes beyond the other bringing cold material in the mantle, this is called subduction, the compression create mountains and volcanic areas on the the slab above and the subductuded slab is buried in the mantle.

This sinking in is compensed by the rising of warm material in the volcanic zones and the oceanic ridges.

Very soon those movements were explained by convection movements in the mantle, but the size and the geometry of those movements is still not very well known.
Two main hypothesis exist:

one suggests the existence of two separated zones of convection, one in the upper mantle and an other in the inferior mantle, this last zone would be occupied by bigger cells of convection.
the other suggests that the convection cells would take place in all the mantle, up to the depth of 2900 Km.

This circulation enables the earth to dissipate the heat trapped in it when the planet was created and the one resulting from the desintegration of the radioactifs elements like uranium , thorium or potassium.

The two zones of the mantle:

These two zones were detected thanks to sismic waves propagation studies: the wave speed changes at around 670 km where the materials structure changes, the more stable materials are the perovskite silicates, Fe, Mg.

At first sight, it could sound surprising that a cristallin solid could be animated of convection movements.

In fact, the mantle behaves like a fluid of infinite viscosity: this material is almost solid but still capable to flow at the geologic temporal scale with a dynamic viscosity of about 10^21 poiseuilles.

The theory of convection in the mantle:

Like a solid, a fluid can conduct heat by conduction, but it can also transport it thanks to the movement of its particles, this is called advection.

Here, this is the difference of temperature between the top and the bottom of the domain that generates the movement: when a body becomes warmer, it gets lighter and as a result starts rising.
As it is rising it is surrounded by colder bodies and get colder, heavier and so stops rising.
This movement is in competition with the strengh of viscosity and the natural gradient of temperature set by the thermal conduction.

Those three effects are summed up by the Rayleigh number, when it gets bigger than a critic value, the system becomes unstable and the particles start moving.

Henri Bénard (1900) and Lord Rayleigh (1916) established the equations of convection but when it comes to considering the all mantle, the problem gets more complex.
In fact, the radioactif elements generate heat as they decompose and the compressibility of the rocks, or phases changes transform the equations system in a non linear coupled system hard and expensive to solve.

The consequences of the convection movements : magma

The crust is mainly composed of granit, we have numerous samples of this zone. In the mantle, basalts are the most present, they reach the surface as magma, producted by the fusion of the periodites that are the main constituant of the mantle.
This fusion takes place about 200 km deep beyond the surface and results from the fast rising of the periodites where the convection movements create acsendant movements to the surface.
The important pressure on the rocks decrease faster than the temperature, what allows the fusion and the creation of a magma.
When the rocks of the mantle melt, the different chemical elements separate in a liquid and a solid fraction depending on their affinity for the magmatic liquids.The mantle is the rest of the continental extraction , privated from by the departure of the magmaphiles elements.

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