A novel method for analyzing the global stability of inviscid columnar swirling flow in a finite pipe

作者：Wang S^*

来源：Physics of Fluids, 2008, 20(7): 074101.

DOI：10.1063/1.2939389

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. Using the new method, we investigated the energy transfer mechanism of the Lamb-Oseen vortex in a finite pipe and revealed a new energy transfer mechanism related to the flow stability.

• 出版日期2008-7