CHALLENGING problem facing theoretical combustion aerodynamicists today is the prediction of turbulent reacting swirl flows. Prediction greatly facilitates economical design and operation of combustion systems, where flame size, shape, stability, and combustion intensity are often controlled by the use of, among other things, swirl.1 The degree of swirl is characterized by the swirl number S (axial flux of angular momentum divided by the axial flux of axial momentum times nozzle radius), or the local swirl number Sz (which uses the local mixing layer width). The swirl strength determines the degree of upstream influence. The flow classification of parabolic (boundary-layer type with a single predominant direction—weak swirl S 0.6), governs the type of boundary conditions required and the solution method. Marching methods are appropriate for the former; relaxation methods for the latter.2 Recent work in the simulation and solution of these flows is reviewed in Ref. 3 and the full-length paper.