An afterburner apparatus that utilizes a novel swirl generator for rapidly and efficiently atomizing, vaporizing, as necessary, and mixing a fuel and an oxidant. The swirl generator converts an oxidant flow into a turbulent, three-dimensional flowfield into which the fuel is introduced. The swirl generator effects a toroidal outer recirculation zone and a central recirculation zone, which is positioned within the outer recirculation zone. These recirculation zones are configured in a backward-flowing manner that carries heat and combustion byproducts upstream where they are employed to continuously ignite a combustible fuel/oxidizer mixture in adjacent shear layers. The recirculation zones accelerate flame propagation to allow afterburning to be completed in a relatively short length. Inherent with this swirl afterburner concept are design compactness, light weight, lower cost, smooth and efficient combustion, high thrust output, wide flammability limits, continuous operation at stoichiometric fuel/oxidizer mixture ratios, no combustion instabilities, and relatively low pressure losses.