Spectral characteristics of unstable modes of a free vortex

Akhmetov V. K.

Swirling flow with a velocity profile of the Batchelor vortex type has been studied on the basis of the linear hydrodynamic stability theory. An effective numerical method for solving the spectral problem has been developed. This method includes the asymptotic solutions at artificial and irregular singular points. For fixed values of the Reynolds numbers, the curves of neutral stability are plotted. Branching points of unstable modes are found.

Keywords:swirling flow, hydrodynamic stability, spectral problem, neutral curves, singular points.