Typically, Rayleigh-Benard instabilities occur when you consider a viscous
fluid (conducting heat) placed between two plates at different temperatures.

If
the bottom plate is cooler than the upper one (T2<T1), the system is
stable as buoyancy forces and gravitational forces are acting in the same
direction.

When
the bottom plate is hotter than the upper plate, there can be an apparition
of Rayleigh-Benard instabilities, partly depending on the temperature difference
between the two plates and the distance between the two plates. Indeed,
with a sufficient temperature difference, the particles at the bottom gets
hot enough to rise up (buoyancy forces are strong enough to push up the
particles), whereas the coldest ones tend to fall with the effects of the
gravity, then heat at the contact of the hot layer and so rise up again
leading to the formation of non stable convective rolls, as can be seen
in the following visualization.

To study this kind of phenomenon, it is interesting to consider the Rayleigh number which is an indicator of the vigor of the convection. It is defined as follows:

In
fact, even if the hottest plate is under the coldest one, the system can
be stable. In fact, instabilities occur from a certain temperatues difference,
ie a certain Rayleigh number. In fact, a particule is under the influence
of two opposite forces: buoyancy forces (destabiliting forces) and draft
forves (stabilisating forces). When the buoyancy forces get high enough
compared to the draft forces, the system is not stable anymore. This theorically
occurs after a **critical Rayleigh number of 1708.**