A numerical technique is developed for solving axisymmetric, incompressible, turbulent swirling flow problems. The Reynolds stresses are expressed in terms of a scalar turbulent viscosity, μt = ρCμk2/ε. The turbulent kinetic energy, k, and ε, the turbulent energy dissipation rate, are obtained by solving the corresponding transport equations; Cμ is an empirical constant. Flow calculation results are presented for the coaxial flow configuration shown in Fig. 1. Of particular interest is the presence of flow recirculation due to vortex breakdown. Effects of inner and outer swirl, axial velocity ratio and Reynolds number on the formation, size, and location of the recirculation zone are considered.