SINGULAR MODES IN RAYLEIGH INSTABILITY OF 3-DIMENSIONAL STREAMWISE-VORTEX FLOWS

The upper-branch neutral modes of inviscid instability in a boundary-l ayer flow with significant longitudinal vortices present are shown to possess typically a logarithmically singular, non-inflectional, critic al layer. This contrasts with previous linear and nonlinear suggestion s implemented in vortex-wave interaction and secondary instability the ories, which are re-examined. The analysis here is based first on pert urbation techniques applied to a Rayleigh unstable planar motion suppl emented by a vortex centred around the inflection level, followed by t he extension to more general cases. Flows with order one and larger sp anwise scales are considered. Multiple solutions, their limit properti es and parametric continuations are illustrated with concrete examples .