Cross-flow vortices and their secondary instability in Falkner-Skan-Cooke boundary layers.

Authors: Högberg, M., Henningson, D.S.H.
Document Type: Report
Pubstate: Published
Journal: FFA-TN 1996-60
Year: 1996


Linear eigenvalue calculations and direct numerical simulations (DNS) of disturb ance growth in Falkner-Skan-Cooke (FSC) boundary layers have been performed. The growth rates of the small amplitude disturbances obtained from the DNS calcu lations show substantial differences compared to linear local theory, i.e. non-p arallel effects are large. This is in agreement with results obtained using the parabolic stability equations (PSE), also presented in this paper. Using single frequency and random disturbances in the DNS we find that the most amplified waves have characteristics in agreement with linear theory. With higher amplitude initial disturbances in the DNS calculations, saturated cr oss flow vortices are obtained. In these vortices strong shear layers appear. When a small random disturbance is added to a saturated cross-flow vortex, a low frequency secondary instability is found located at the bottom shear layer of t he cross flow vortex and a high frequency instability is found at the upper shea r layer of the cross flow vortex. The growth rates of the secondary instabilitie s are found from detailed analysis of simulations of single frequency disturbanc es. The low frequency disturbance is amplified throughout the domain, but with a lower growth rate than the high frequency disturbance, which is amplified only once the cross-flow vortices have reached a level where nonlinear effects have c aused saturation. The high frequency disturbance has a growth rate that is consi derably higher than the growth rates for the primary instabilities.