A swirling jet, emerging normal to a plane, serves as a model of a tornado and is characterized by its flow force and outer circulation. This model is examined here using the full Navier–Stokes equations. Three branches of solutions are found which form a hysteresis loop and a cusp catastrophe that means jump transitions between flow regimes. One of the jumps relates to vortex breakdown and the other relates to a new (opposite) effect: abrupt vortex consolidation. These results are compared with those of Long [J. Fluid Mech.11, 611 (1961)], who considered a near‐axis jet in the boundary layer approximation. More detailed analysis made here for high circulation values allows discovery of two new types of asymptotic solutions corresponding to a near‐plane fan jet and a two‐cell flow. It was also found that the boundary layer approach for the near‐axis jet fails to accurately yield the total flow force because the outer flow contributes a share of the momentum flux of comparable magnitude to that of the inner flow. The prediction of the jump transitions between one‐ and two‐cell flow patterns agrees with observations of abrupt changes in tornado patterns in nature.