The onset of three-dimensionality and time-dependence in Görtler vortices: neutrally stable wavy modes

Recently Hall & Seddougui (1989) considered the secondary instability of large-amplitude Görtler vortices in a growing boundary layer into a three-dimensional flow with wavy vortex boundaries. They obtained a pair of coupled, linear ordinary differential equations for this instability which constituted an eigenproblem for the wavelength and frequency of this wavy mode. In the course of investigating the nonlinear version of this problem (Seddougui & Bassom 1990), we have found that the numerical work of Hall & Seddougui (1989) is incomplete; this deficiency is rectified here. In particular, we find that many neutrally stable modes are possible; we derive the properties of such modes in a high-wavenumber limit and show that the combination of the results of Hall & Seddougui and our modifications lead to conclusions which are consistent with the available experimental observations.