Flow structures and wave-number selection in spiraling vortex flows

Abstract

Spiraling vortices observed in instabilities of annular flows are found as propagating-wave solutions of nonsymmetric amplitude equation. The damping of the wave near the ends of the vortex system results in a selection of the wave number through a new mechanism. The distance of the wave number q to the critical one $q_c$ is shown to be q-$q_c$=O(ε), where ε is the small relative distance to threshold. This result is supported by theoretical and numerical arguments, and confirmed by experiment.