Linear stability analysis of cylindrical flames

This article is concerned with the linear stability of cylindrical flames in a velocity field generated by a line source of fuel of constant strength $2\pi \kappa$ per unit length. The mathematical model involves the equations of mass and heat transfer in the regions on either side of the flame sheet and a set of jump conditions across the flame sheet. It admits a basic solution representing a stationary flame front in the shape of a circular cylinder at a radial distance $\kappa$ from the line source. The circular front loses stability if either (i) the Lewis number of the reaction-limiting component is less than some critical value less than 1 and $\kappa$ is greater than a critical value, or (ii) the Lewis number is greater than a critical value greater than 1. In the former case the circular front evolves into a steady cellular front, in the latter into a pulsating front, which may also be cellular. The WKB method is employed to derive approximations for the pulsating and cellular branches of the neutral stability curve.