The stability of swirling flows at large Reynolds number when subjected to disturbances with large azimuthal wavenumber

An asymptotic theory is developed to describe the stability characteristics of a swirling axial flow at high Reynolds number R when subject to disturbances with a large azimuthal wavenumber n. It is based on an earlier study by Leibovich and Stewartson of the corresponding inviscid problem. The essence of the theory is to exploit the fact that the disturbance is concentrated on a narrow band at a finite distance from the axis decaying exponentially on either side. As an example to illustrate the theory, the stability characteristics of a trailing vortex is examined. A comparison with computed values of the neutral curves for n=1,2,3 shows that even at such low values of n the theory is generally qualitatively correct and in some respects is remarkably accurate. UFoff