Collapse, symmetry breaking, and hysteresis in swirling flows

The paper reviews striking features of swirling flows-collapse, swirl gener ation, vortex breakdown, hysteresis, and axisymmetry breaking-and the mecha nisms involved with the help of conical similarity solutions of the Navier- Stokes equations. The strong accumulation of axial and angular momenta, obs erved in tornadoes and Bows over delta wings, corresponds to collapse, i.e. the singularity development in these solutions. Bifurcation of swirl expla ins the threshold character of swirl development in capillary and electrovo rtex flows. Analytical solutions for fold catastrophes and hysteresis revea l why there are so few stable states and why the jump transitions between t he states occur-features typical of tornadoes, of flows over delta wings, a nd in vortex devices. Finally, the divergent instability explains such effe cts as the splitting of a tornado and the development of spiral branches in tree and near-wall swirling flows.