Introduction


 

       We want to study the stability of a fluid situated between two plane and horizontal plates maintained at two different
temperatures. Each plate is maintained at an uniform temperature and the fluid is considered as having a weight.
We try to evaluate the conditions and the nature of the convective movements of the fluid.
       In the case that the up plate has a temperature higher than the temperature of the down plate, the thermal stratification
is stable. In this case, a particle of fluid moved to up will go in a zone where the volumic mass is less important. The strength
of weight will thus play a role of stabilization since it will tend to bring back the particle to its initial position.
        If we consider the inverse situation, where the up plate is colder than the down plate, the fluid more heavy will be over the
lighter fluid. The action of the weight will have an effect of destabilization on the system. The particles of the down will tend to
go up under the effect of the forces of flottability and the particles of the up will tend to go down under the action of the weight.
The thermic stratification will be then unstable.
       When the gradient of temperature is over a critical value we can observe between the two plates the appearance of rolls of
convection. This phenomenon is called the Rayleigh-Bénard  instability and it is quantified by an adimensional number
called number of Rayleigh (Ra) .