Numerical Study on Mechanism of Small Vortex Generation in Boundary Layer Transition

The small vortex generation is a key issue of the mechanism for late flow transition and turbulence generation. It was widely accepted that small length vortices were generated by large vortex breakdown. According to our recent DNS, we find that the hairpin vortex structure is very stable and never breaks down to small pieces. On the other hand, we recognize that there are strong positive spikes besides the ring neck in the spanwise direction. The strongly positive spikes are caused by second sweeps which are generated by perfectly circular and perpendicularly standing vortex rings. The second sweep brings energy from the invisid region downdraft to the bottom of the boundary layers, which generates high shear layers around the positive spikes. Since the high shear layer is not stable, all small length scales (turbulence) are generated around high shear layers especially near the wall surface (bottom of boundary layers). This happens near the ring neck in the streamwise direction and besides the original vortex legs in the spanwise direction. The small length scales then rise up from the wall surface and convect to the upper boundary layer. Therefore, the small length scales (turbulence) are not generated by " large vortex breakdown " , but by " high shear layers " produced by the positive spikes and the wall surface. Nomenclature  M = Mach number Re = Reynolds number in  = inflow displacement thickness w T = wall temperature  T = free stream temperature in Lz = height at inflow boundary out Lz = height at outflow boundary Lx = length of computational domain along x direction Ly = length of computational domain along y direction in x = distance between leading edge of flat plate and upstream boundary of computational domain d A 2 = amplitude of 2D inlet disturbance d A 3 = amplitude of 3D inlet disturbance  = frequency of inlet disturbance 2 3 d d ,   = two and three dimensional streamwise wave number of inlet disturbance  = spanwise wave number of inlet disturbance R = ideal gas constant  = ratio of specific heats   = viscosity