HYSTERESIS IN A SWIRLING JET AS A MODEL TORNADO

A swirling jet, emerging normal to a plane, serves as a model of a tor nado and is characterized by its flow force and outer circulation. Thi s model is examined here using the full Navier-Stokes equations. Three branches of solutions are found which form a hysteresis loop and a cu sp catastrophe that means jump transitions between flow regimes. One o f the jumps relates to vortex breakdown and the other relates to a new (opposite) effect: abrupt vortex consolidation. These results are com pared with those of Long [J. Fluid Mech. 11, 611 (1961)], who consider ed a near-axis et in the boundary layer approximation. More detailed a nalysis made here for high circulation values allows discovery of two new types of asymptotic solutions corresponding to a near-plane fan je t and a two-cell flow. It was also found that the boundary layer appro ach for the near-axis jet fails to accurately yield the total flow for ce 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 o bservations of abrupt changes in tornado patterns in nature.