The stability of a trailing line vortex. Part 1. Inviscid theory

Abstract

The inviscid stability of swirling flows with mean velocity profiles similar to that obtained by Batchelor (1964) for a trailing vortex from an aircraft is studied with respect to infinitesimal non-axisymmetric disturbances. The flow is characterized by a swirl parameterqinvolving the ratio of the magnitude of the maximum swirl velocity to that of the maximum axial velocity. It is found that, as the swirl is continuously increased from zero, the disturbances die out quickly for a small value ofqifn= 1 (nis the azimuthal wavenumber of the Fourier disturbance of type exp{i(αx+nϕ − αct)}); but for negative values ofn, the amplification rate increases and then decreases, falling to negative values atqslightly greater than 1·5 forn= −1. The maximum amplification rate increases for increasingly negativenup ton= −6 (the highest mode investigated), and corresponds toq≃ 0·85. The applicability of these results to attempts at destabilizing vortices is briefly discussed.