SECONDARY INSTABILITY OF CROSS-FLOW VORTICES IN FALKNER-SKAN-COOKE BOUNDARY-LAYERS

Linear eigenvalue calculations and spatial direct numerical simulation s (DNS) of disturbance growth in Falkner-Skan-Cooke (FSC) boundary lay ers have been performed. The growth rates of the small-amplitude distu rbances obtained from the DNS calculations show differences compared t o linear local theory, i.e. non-parallel effects are present. With hig her amplitude initial disturbances in the DNS calculations, saturated cross-flow vortices are obtained. In these vortices strong shear layer s appear. When a small random disturbance is added to a saturated cros s-flow vortex, a low-frequency mode is found located at the bottom she ar layer of the cross-flow vortex and a high-frequency secondary insta bility is found at the upper shear layer of the cross-how vortex. The growth rates of the secondary instabilities are found from detailed an alysis of simulations of single-frequency disturbances. The low-freque ncy disturbance is amplified throughout the domain, but with a lower g rowth rate than the high-frequency disturbance, which is amplified onl y once the cross-flow vortices have started to saturate. The high-freq uency disturbance has a growth rate that is considerably higher than t he growth rates for the primary instabilities, and it is conjectured t hat the onset of the high-frequency instability is well correlated wit h the start of transition.