On vortex/wave interactions. Part 2. Originating from axisymmetric flow with swirl

Abstract

Following the study in Part 1 of cross-flow and other non-symmetric effects on vortex/wave interactions in boundary layers, the present Part 2 applies the ideas of Part 1 and related works to an incident axisymmetric flow supplemented by a small swirl or azimuthal velocity. This is with a view to possibly increasing understanding of vortex breakdown. The wave components involved are predominantly inviscid Rayleigh-like ones. The presence of the swirl leads to extra features and complications associated mainly with extra logarithmic contributions but for the dominant interactions essentially the same equations as in Part 1 are found. These dominant nonlinear interactions must be based on azimuthal wavenumbers of ± 1 in the case of the Squire jet with swirl. In contrast to Part 1, which consisted mainly of an analysis of the quasi-bounded solutions, a representative set of numerical solutions of the full integro-differential amplitude equations is presented, for realistic axial and swirl velocity profiles. The work points also to the influence of further increases in the incident swirl.