Swirling flow fields in combustion chambers can be determined based on swirl ratio and a velocity profile specified along some path to the vortex center. A method is presented whereby flow fields can be constructed by applying the continuity equation in a streamline coordinate system and imposing irrotationality about the symmetry axis of the vortex ring. The swirl ratio may be specified at the vortex core, along with a velocity profile along any semi-axis of the vortex cross section.