Vortex formation and stability analysis for shear flows over combined spatially and temporally structured walls (Q1970056)

Summary: Benney's theory of evolution of disturbances in shear flows over smooth and flat boundary is extended to study of shear flows over combined spatially and temporally corrugated walls. Perturbation and multiple scales analyses are employed for the case where both amplitude of the corrugations and the amplitude of wave motion are small. Analyses of instability of modulated mean shear flows with respect to spanwise-periodic disturbance rolls and of the subsequent vortex formation and vortex stability are presented, and the effects of the corrugated walls on the resulting flow and vortices are determined. It is found that particular corrugated walls can originate and control the longitudinal vortices, while some other types of corrugated walls can enhance instability of such vortices.