The Darrieus-Landau instability of premixed flames

The most prominent intrinsic flame instability is the hydrodynamic, or Darrieus-Landau (DL) instability, that results from the gas expansion caused by the heat released during combustion, which induces hydrodynamic disturbances that enhance perturbations of the flame front. The DL instability has many ramifications in premixed combustion; it promotes the creation of corrugated flames with relatively sharp edges pointing towards the burned gas. In this presentation, we first review the developments that led to a better understanding of the roles of viscosity, heat conduction and species diffusion on the flame stability. This includes the work of Markstein that attempted to phenomenologically improve the Darrieus and Landau analyses, and the asymptotic studies that provided an explicit dependence on the physical parameters. We then discuss the nonlinear flame development starting with the weakly-nonlinear analytical studies and proceeding with the more recent fully-nonlinear numerical results. We show that, unlike the implication that may be inferred from the original publications of Darrieus and Landau that premixed flames as a result of the instability will always appear as turbulent flames, the instability leads to the formation of cusp-like conformations with elongated intrusions pointing toward the burned gas region. These structures are stable and, because of their larger surface area, propagate at a speed that is substantially faster than the laminar flame speed. Finally, we show that the DL instability remains relevant in turbulent flames, but their influence appears limited to weak-to-moderate turbulence intensity flows.