PRIMARY AND SECONDARY INSTABILITIES OF THE ASYMPTOTIC SUCTION BOUNDARY-LAYER ON A CURVED PLATE

The temporal growth of Gortler vortices and the associated secondary instability mechanisms are investigated numerically in the case of an asymptotic suction boundary layer on a curved plate. Highly inflectional velocity profiles are generated in both the spanwise and vertical directions. The inflectional velocity profile develops earlier in the spanwise direction. There exist two distinct modes of instability that eventually lead to the breakdown of Gortler vortices: the sinuous mode and the varicose mode. The temporal secondary instability analysis of the three-dimensional inflectional velocity profile reveals that the sinuous mode becomes unstable earlier than the varicose mode. The sinuous mode is shown to be primarily related to shear in the spanwise direction, partial derivative U/partial derivative z, and the varicose mode to shear in the vertical direction, a partial derivative U/partial derivative y.