Spinning Waves in Gaseous Combustion

We consider a diffusional-thermal model describing the combustion of a premixed gas in a cylindrical domain. We show that a uniformly propagating plane flame is unstable when the Lewis number L exceeds a critical value Lc. We employ a nonlinear analysis to show that for L > Lc various types of solutions bifurcate from the uniformly propagating plane flame. The bifurcated solutions describe pulsating flames whose spatial distribution corresponds to combinations of axial, radial and tangential modes. The tangential modes are of two types, corresponding to standing waves on, and to travelling waves propagating in both clockwise and counterclockwise directions around, the cylinder. The latter describe spinning waves in which a hot spot (or spots) (local temperature maximum) propagates in a helical motion around the axis of the cylinder. Both single and multi-headed spins are obtained.