Instability of a free swirling jet driven by a half-line vortex

By studying similarity solutions of the Navier-Stokes equations, which repr esent swirling jets of a viscous incompressible fluid, we develop a new sta bility approach, and elucidate the nature of perturbations that cause hyste resis and break axisymmetry. As an example, we consider a jet in an infinit e fluid driven by a half-line vortex: a model of a tornado and of a leading -edge vortex above the delta wing of an aircraft. The approach reduces the problem of spatial stability of these strongly non-parallel flows to an ord inary differential system and thereby eases the analysis. We show how non-u niqueness of the solutions appears through cusp and fold catastrophes as th e swirl Reynolds number, Re-s, increases, and find that the fold instabilit y is due to disturbances at the outer boundary of the flow. Also, we study the breaking of axisymmetry due;to steady three-dimensional disturbances, a nd reveal that a helical instability occurs due to disturbances at the inne r boundary of the how. Both the fold and helical instabilities occur for mo derate values of Re-s. Finally, we deduce an amplitude equation, similar to the Ginzburg-Landau eq uation, to describe the weakly nonlinear spatio-temporal growth of disturba nces when Re-s is slightly above its critical value for linear stability. T hus, our results reveal new features of axisymmetric and helical vortex bre akdown in jets.