On the onset of three-dimensionality and time-dependence in Görtler vortices

Abstract

The secondary instability of large-amplitude Görtler vortices in a growing boundary layer is discussed in the fully nonlinear regime. It is shown that the three-dimensional breakdown to a flow with wavy vortex boundaries, similar to that which occurs in the Taylor vortex problem takes place. However, the instability is confined to the thin shear layers which were shown by Hall & Lakin (1988) to trap the region of vortex activity. The disturbance eigenfunctions decay exponentially away from the centre of these layers, so that the upper and lower shear layers can support independent modes of instability. The structure of the instability, in particular its location and speed of downstream propagation, is found to be entirely consistent with recent experimental results. Furthermore, it is shown that the upper and lower layers support wavy vortex instabilities with quite different frequencies. This result is again consistent with the available experimental observations.