The critical state: a trapped wave model of vortex breakdown

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Abstract
A model of vortex breakdown is presented and its predictions compared with the experiments of Sarpkaya (1971). The model is cntred about a theory of long, weakly nonlinear waves propagating on critical flows in tubes of variable cross-section. Although the weakly nonlinear theory must be extended beyond its domain of formal validity, many of the experimentally observed features of vortex breakdown are reproduced by the model. The description of the time evolution of the flow field that is presented requires numerical calculations that are not simple, but some important conclusions may be determined by easy computations. In particular, the axial position of a breakdown may be found from a very simple equation (10).