Abstract:
We developed a general strategy to study the stability problem of the inviscid columnar swirling flow in a finite pipe based on the perturbation method of linear operators. By virtue of the columnar base state we were able to derive all the necessary formulas used in perturbation method in a manner of separation of variables. We then conduct a necessary benchmark case study based on the solid body rotation flow. We then applied the general method to the Lamb-Oseen vortex and the q-vortex, and found their approximated growth rate functions. The perturbation method proved effective and robust in application to these vortex flows. We also extended the method, by using the analytic continuation, to find the unstable modes with complex growth rates. This analytic continuation method reflects the global nature of the perturbation method. This study fills a major gap in the study of the global stability for swirling flows, and will have a positive impact on the study of the vortex breakdown phenomenon.
