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.

We report on a set of turbulent flow experiments of the Taylor type in which the fluid is contained between a rotating inner circular cylinder and a fixed concentric outer cylinder, focusing our attention on very large Taylor number values, i.e. \[ 10^3 \leqslant T/T_c \leqslant 10^5, \] where Tc is the critical value of the Taylor number T for onset of Taylor vortices. At such large values of T, the turbulent vortex flow structure is similar to the one observed when T – Tc is small and this structure is apparently insensitive to further increases in T. These flows are characterized by two widely separated length scales: the scale of the gap width which characterizes the Taylor vortex flow and a much smaller scale which is made visible by streaks in the form of a ‘herring-bone’-like pattern visible at the walls. These are conjectured to be Görtler vortices which arise as a result of centrifugal instability in the wall boundary layers. Ideas of marginal instability by which we postulate that both the Taylor and Görtler vortex structures are marginally unstable on their own scale seem to provide good quantitative agreement between predicted and observed Görtler vortex spacings.

The stability of pipe Poiseuille flow with respect to linear azimuthally periodic disturbances is investigated. It is found that many radial modes of disturbance exist for each azimuthal periodicity. No linear instability is found for the mode sets with azimuthal periodicity of one.

No abstract

In a previous paper, the inviscid stability of a swirling far wake was investigated, and the superposition of a swirling flow on the axisymmetric wake was shown to be initially destabilizing, although all modes investigated eventually become more stable at sufficiently large swirl. The most unstable disturbances were non-axisymmetric modes with negative azimuthal wavenumber n representing helical wave paths opposite in sense to the wake rotation. The disturbance growth rate appeared to increase continuously with |n|, while all modes with |n| > 1 represented disturbances which are completely stable for the non-swirling wake. In the present analysis, both timewise and spacewise growth rates are calculated for the lowest three negative non-axisymmetric modes (n = −1, −2 and −3). Vortex intensity is characterized by a swirl parameter q proportional to the ratio of the maximum swirling velocity to the maximum axial velocity defect. The large wavenumbers associated with the disturbances at large |n| allow the n = −1 mode to have the minimum critical Reynolds number of 16 (q ≃ 0·40). The other two modes investigated have minimum Reynolds numbers on the neutral curve of 31 (n = −2, q = 0·60) and 57 (n = −3, q = 0·80). For each mode, the neutralstability curve is shown to shift rapidly towards infinite Reynolds numbers once the swirl becomes sufficiently large. Some of the most unstable swirling flows are shown to possess spacewise amplification factors almost ten times that for the most unstable wavenumber for the non-swirling wake at moderate Reynolds numbers.