Note on the Nonlinear Stability of Inviscid Swirling Flows

Abstract

In this work, we investigate the nonlinear stability of an inviscid, incompressible, homogeneous fluid in an annular region bounded by two coaxial cylinders. Using Arnold’s method, we derive two general stability theorems for steady basic flows subjected to two-dimensional normal-mode disturbances. The theoretical findings are illustrated with representative examples of swirling flows.