Towards Understanding of Natural Boundary-Layer Transition for Low-Speed Flows via Random Excitation

The objective of this research is to contribute towards the understanding of ‘natural’ laminar-turbulent transition in low-speed zero-pressure-gradient boundary layers, where transition is initiated by random excitation. Toward this end, linear Secondary Instability Analysis (SIA) and Direct Numerical Simulations (DNS) are employed to investigate the effects of randomized external disturbances with a broad range of frequencies and wavenumbers on the linear and nonlinear stages of boundary-layer transition. In the present study, very low level vortical free-stream turbulence (FST) fluctuations are introduced at the inflow boundary. Since the leading-edge is not included in our simulations, the receptivity process to the FST is replaced by introducing small amplitude random disturbances generated by specifying a wall-normal velocity component across a narrow slot at the wall. This approach will allow the flow to naturally ‘select’ the relevant frequencies and wavenumbers from the broadband free-stream disturbances, which can then amplify and interact nonlinearly, and then ultimately lead to transition. The SIA results indicate that the random excitation creates randomized Tollmien-Schlichting (T-S) waves, reminiscent of the “modulated wave-trains” observed by Schubauer and Skramstad (Laminar-boundary-layer oscillations and transition on a flat plate :909, 1948 [1]) in their ‘natural’ transition experiments. Both the linear SIA and the DNS results indicate that subharmonic resonance is the dominant secondary instability mechanism. An unexpected finding from the DNS data is that in the nonlinear stages of the transition process tertiary vortices appear which are attached to the legs of the lambda structures. These tertiary structures seem to be linked to the disturbances with a frequency range that is orders of magnitude higher than the one associated with T-S waves. These preliminary results may hint that an inviscid instability mechanism may play a role in the development of these tertiary structures.