Vortex Kelvin Modes with Nonlinear Critical Layers

Abstract

When helical neutral modes propagate on a vortex with a continuous velocity profile the inviscid equation governing linear stability theory may have a singular critical point at some value of r, the radial coordinate. Viscosity or temporal evolution can be restored locally to treat the critical layer centered on this singular point. Nonlinearity, however, is a more appropriate choice in applications where the Reynolds number is large. The associated theory is outlined in this paper and new solutions to the eigenvalue problem are presented.