Transition to turbulence by interaction of free-stream and discrete mode perturbations

Abstract

Mixed mode transition is studied by direct numerical simulation. Low frequency streaks are induced within the boundary layer by free-stream turbulence and an Orr-Sommerfeld discrete mode eigenfunction is introduced at the inlet. Amplitudes are selected such that the interaction of these modes can cause transition. Aside from the highest amplitude of free-stream turbulence, neither disturbance alone is sufficient to cause transition within the flow domain. Results are classified into three routes to transition, depending upon the 2D Tollmien-Schlichting (TS) mode strength and free-stream turbulence intensity. (1) At low turbulence intensities, secondary instabilities instigate transition. On a strong TS mode, Λ vortices develop, but they are neither H nor K type. The pattern and spanwise size of Λ vortices depend upon the frequency and spanwise width of Klebanoff streaks by which they are generated. (2) When the TS mode amplitude is low, transition is via streak breakdown. The streaks are induced by the free-stream turbulence, but this case differs from conventional bypass transition in the mechanism of inception of turbulent spots. Three dimensional visualizations of the perturbation flow field show growing, helical undulations similar to n = 1 instability modes observed in axisymmetric jets and wakes. (3) At high turbulence intensities, the flow undergoes bypass transition. The TS wave has a small effect, but its influence is seen at the larger of the two amplitudes studied.