$\star$ Instabilities of Pram-Darrieus

If one observes the flame on scales larger than his thickness, the structure of the flame on the level of combustions and diffusion can be neglected and the approximated flame as a jump of density which is propagated with a normal speed: the laminar speed of the flame.

The mean approximation of `` flame '' authorizes a linear analysis of the stability of the face compared to space disturbances. The result of this analysis due to Landau and Darrieus indicates that the thin flames are linearly unstable on all the scales.

In the context of the deflagrations, this type of instabilities involves an enlarging of the disturbances until the formation of a structure in cell which extends the surface of the face of combustion. This type of disturbance does not involve turbulence and prevents a significant acceleration of the flame.

However, it is possible that with low density stabilization is broken with significant effects on the deflagration.