Cylinder instability in bounded flow with constant vorticity

摘要

The stability of the system consisting of an inner moving cylinder, an outer fixed cylinder and circular flow with constant vorticity between them is considered. Solution of the problem is obtained in form of a Loran series with respect to the distance between axis of inner and outer cylinder. The solution can be obtained with any given accuracy by including more terms in Loran series. The Lagrangian of the system is obtained and the analysis of the system stability with respect to non-linear approximation is derived.