A method for mathematically solving the oscillatory infinite reaction rate diffusion flame is extended to the case where the oscillating convective coflow is either inside of, or adjacent to, a viscous vortex. The neglect of streamwise diffusion coupled with the restriction to infinite
rate chemistry produces a Burke-Schumann boundary layer flame. The mathematical transformation, which does not require a priori restriction to small coflow oscillations, renders the transient oscillatory problem equivalent to a steady-state problem that can be solved mathematically
and numerically evaluated to a high degree of accuracy. Flow fluctuations that are large fractions of the initial flow field are described exactly. Features of the flame response are examined without recourse to detailed time-dependent numerical simulations. There is no need to perform any
small-perturbation analyses. The method is applied to examine the influences of the bulk inflow speed, the bulk inflow oscillation rate, and the interaction of the inflow and its oscillation rate with the viscous vortex.
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