The wake of a finite cylinder with free ends and an aspect ratio of 21
.4 is simulated in three-dimensions and analysed theoretically. Close
to the primary-instability threshold, the flow is shown to settle on a
limit cycle with a uniform frequency throughout the flow-field. About
20% above the primary-instability threshold, a secondary instability
sets in and the limit cycle becomes unstable. The new attractor of the
flow can be identified as a limit T-2-torus characterized by two inco
mmensurate frequencies. One of them is shown to evolve continuously fr
om the primary-instability frequency, the other one, about 17 times sm
aller near the secondary-instability threshold, generates a slow modul
ation of the oscillations in the wake. The limit cycle and the limit t
orus are described in terms of their Fourier expansion and the spatial
distribution of the most relevant Fourier components is investigated.
The theoretical analysis and numerical results given shed some light
on the mechanisms underlying a number of known but not satisfactorily
explained three-dimensional effects in wakes of finite cylinders such
as the ambiguity in the dominant Strouhal frequency, the existence of
zones with different frequencies spanwise in the wake, the discretenes
s of coexisting frequencies observed in the wake as well as the spatia
l uniformity of the beating period. They moreover explain the Reynolds
number variation of these effects and identify the recirculation arou
nd the cylinder ends as basically responsible for the onset of the sec
ondary instability. The results are compared to the case of a cylinder
with aspect ratio of 10.7 to determine the basic trends in aspect rat
io dependence. It is shown that qualitatively the same behaviour is ob
tained, but that the secondary-instability threshold is shifted signif
icantly upward to about twice the primary-instability threshold. Simul
ations of the wake of a finite NACA wing with incidence show that the
form of the cross-section plays a minor role.