Development of the instability of an axisymmetric vortex flow in a circular cylinder

Abstract

A vortex structure consisting of two concentric vortex rings located in a circular cylinder is studied. The rings touch each other and have a uniform vorticity. The geometric and dynamic parameters of the rings satisfy the condition of zero total intensity. A linear stability analysis of this structure is performed, including the limiting cases when the inner ring transforms into a circle or the outer ring is adjacent to the boundary of the cylinder. The results of numerical simulation of the evolution of unsteady flows are presented for a wide range of variation of governing parameters of the problem. It is established that the evolution of unstable vortex flows results in the formation of several types of quasistationary structures, the topology of which depends mainly on the dominant disturbance mode.