On the fast-time oscillatory instabilities of Linan's diffusion-flame regime

Fast-time instability for diffusion flames, with Lewis numbers set equal for fuel and oxidizer but greater than unity, is numerically analysed by the activation energy asymptotics and Evans function method. The time and length scales being chosen to be those of the inner reactive-diffusive layer, the problem corresponds to the instability problem for the Linan's diffusion-flame regime. The instability is primarily oscillatory and emerges prior to reaching the turning point of the characteristic C-curve, usually known as the Linan's extinction condition. A critical Lewis number, L,, is also found, across which the instability changes its qualitative character. Below L,, the instability possesses primarily a pulsating nature in that the two real branches of the dispersion relation existing for small wave numbers merge at a finite wave number, from which a pair of complex conjugate branches bifurcate. The maximum growth rate is found at the zero wave number. For Lewis numbers greater than L., the eigensolution branch for small reactant leakages is found to be purely complex with the maximum growth rate found at a finite wave number, thereby exhibiting a travelling nature. As the reactant-leakage parameter is further increased, the instability characteristics turns into a pulsating type, similar to that for 1 < L < L-c. The switching between different instability characters is found to correspond to the Bogdanov-Takens bifurcation.