Direct numerical simulation of instability of zero-pressure-gradient boundary layer over three-dimensional corrugated wall

The influences of surface corrugation with small amplitude on zero-pressure-gradient boundary layer instability were examined numerically by solving the three-dimensional compressible Navier-Stokes equations. Three-dimensional sinusoidal corrugations, with amplitude less than 10% of the boundary layer thickness and wavelengths nearly the same as that of Tollmien-Schlichting (T-S) wavelength, were considered. The results showed that the basic flow near the surface followed the corrugated surface without any separation and low- and high-speed streaks were formed in the middle of the boundary layer. The three-dimensional surface corrugation had little influence on the growth of T-S waves compared to two-dimensional surface corrugation, that is, the growth rate of T-S wave was almost the same as that of smooth wall case. Amplitude of energy production in the three-dimensional corrugation case was found to be about half of that in the two-dimensional case while energy diffusion remained nearly the same in both cases. It was also found that the transient distance of change in surface geometry from smooth wall to three-dimensional corrugation wall was only about one corrugation wavelength