Author(s)

A. Ni

Abstract

Complete mathematical similarity between nonlinear transcritical transitions in swirled flows and transonic phenomena in compressible gas dynamics is established. It is shown that transition of base supercritical columnar swirling flow to another subcritical columnar swirling flow is governed by an equation identical to that of the shock waves formation in gases. It is proven that under some assumptions transition follows the scenario suggested by Benjamin [1]. The presented study is based on the nonlinear wave theory of swirled flows developed by Leibovich [7]. The results are established through a rigorous mathematical analysis and provide a solid theoretical understanding of the wave dynamics of axisymmetric swirling flows. The unsteady wave analysis suggests a consistent explanation of the mechanism leading to the axisymmetric vortex breakdown phenomenon

Keywords