Transition and mixing in impulsively started jets and vortex rings

Abstract

A new method is used to analyze transition in impulsively started jets and vortex rings. The method uses similarity variables to reduce the equations for unsteady particle paths to a quasi-autonomous system with the Reynolds number as a parameter. The flow pattern is represented in terms of the phase portrait of this system and the structure of the flow is defined by its critical points. Flow transition is examined in terms of bifurcations in the topology of the phase portrait which occur as the Reynolds number is increased. There is no assumption that the flow is parallel or that it is subjected to small disturbances. The method of analysis, through straightforward, is new and lies outside the usual small disturbance theory used to determine the stability of various profile shapes.