The object of this BES is studying specific type of hydrodynamic instabilities.

We consider a fluid, initially in equilibrium, between two horizontals and planes plaques at none equal temperatures. At the first sight, there is a linear stationary distribution of temperature depending of Y and not of X and Z, and the fluid keep immobile. Although it's not always the case, because when we raise the difference of the temperature, keeping the bottom temperature greater then the top one, we see the apparition of stationary contrarotatifs rolls. This can be explain with the none equilibrium between stabilisation forces, the drag force, and the destabilisation forces, Archiméde force. the bottom fluid, hot and light, move to the top, In the other hand the fluid on the top, cold and heavy, move to the bottom.

Studying solution stability of Navier-Stock equations make show the existent of a none dimensional number, called critical Rayleigh number, witch characterise the frontier of stability. For Rayleigh number lower then the critical one the flow keeps stable. In the opposite case the flow is unstable.

It's this kind of stability, called the instability of Rayleigh-Benard, that this BES wants to study.

In the other hand there exist of this problem witch give a theoretic critical Rayleigh. This new value will be compared to numerical one found with the simulations. Although in the unstable case, even with the 2D problems and the Boussinesque approximation we didn't find an explicit solution to Navier-Stock equations describing the fluid moving.

This BES, will allow us to familiarise with the use of some computing codes PHOENICS and FLUENT, this codes is generalist and widely used in fluid mechanic domain. For the flows initially immobile we used FLUENT et for the flows with sinusoidal initial condition, we have used PHEONICS.

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