A simple model for the experimentally observed instability of the vortex ring to azimuthal bending waves of wavelength comparable with the core size is presented. Short-wave instabilities are discussed for both the vortex ring and the vortex pair. Instability for both the ring and the pair is predicted to occur whenever the self-induced rotation of waves on the filament passes through zero. Although this does not occur for the first radial bending mode of a vortex filament, it is shown to be possible for bending modes with a more complex radial structure with at least one node at some radius within the core. The previous work of Widnall & Sullivan (1973) is discussed and their experimental results are compared with the predictions of the analysis presented here.

The stability of a helical vortex filament of finite core and infinite extent to small sinusoidal displacements of its centre-line is considered. The influence of the entire perturbed filament on the self-induced motion of each element is taken into account. The effect of the details of the vorticity distribution within the finite vortex core on the self-induced motion due to the bending of its axis is calculated using the results obtained previously by Widnall, Bliss & Zalay (1970). In this previous work, an application of the method of matched asymptotic expansions resulted in a general solution for the self-induced motion resulting from the bending of a slender vortex filament with an arbitrary distribution of vorticity and axial velocity within the core.The results of the stability calculations presented in this paper show that the helical vortex filament has three modes of instability: a very short-wave instability which probably exists on all curved filaments, a long-wave mode which is also found to be unstable by the local-induction model and a mutual-inductance mode which appears as the pitch of the helix decreases and the neighbouring turns of the filament begin to interact strongly. Increasing the vortex core size is found to reduce the amplification rate of the long-wave instability, to increase the amplification rate of the mutual-inductance instability and to decrease the wavenumber of the short-wave instability.

Flow visualization of artificially triggered transition in plane Poiseuille flow in a water channel by means of 10–20 μm diameter tihnium-dioxide-coated mica particles revealed some striking features of turbulent spots. Strong oblique waves were observed both at the front of the arrowhead-shaped spot as well as trailing from the rear tips. Both natural and artificially triggered transition were observed to occur for Reynolds numbers slightly greater than 1000, above which the flow became fully turbulent. The front of the spot moves with a convection speed of about two-thirds of the centreline velocity, while the rear portion moves at about $\frac{1}{3}U_{\rm cl}$. The spot expands into the flow with a spreading half-angle of about 8°. After growing to a size of some 36 times h (the channel depth) at a downstream distance x/h of about 130, the spot began to split into two spots, accompanied by strong wave activity. The spot(s) was followed visually downstream of its origin a distance x/h of about 300. These results indicate that wave propagation and breakdown play a crucial role in transition to turbulence in Poiseuille flow.