Nonlinear response of a laminar boundary layer to isotropic and spanwise localized free-stream turbulence (6th AIAA Theoretical Fluid Mechanics Conference, 2011)
This paper is concerned with the nonlinear response of a pre-transitional flat-plate boundary layer to isotropic and spanwise localized free-stream turbulence (FST). The turbulence is represented as a superposition of Fourier modes and the displacement effect of the boundary layer on FST is taken into consideration. The responses of the boundary layer to FST are low-frequency streamwise streaks, and their development is obtained by numerically solving the nonlinear unsteady boundary-region (NUBR) equations. Direct numerical simulations (DNS) are carried out to validate the results. Nonlinearity is stabilizing in that it reduces the root mean square (rms) of the perturbation velocity in the boundary layer for small FST Reynolds number RL11, while it is destabilizing for large RL11. The issue of upstream-downstream versus top-down mechanisms is investigated. Streaks primarily develop from the upstream forcing; the top-down forcing plays a minor role. The numerical calculations for isotropic FST are compared with DNS results of Ovchinnikov et al. and experimental data of Roach & Brierley. The computed disturbances do not reach the levels in the DNS and experiment. However, good quantitative agreement is obtained when the anisotropy of FST induced by the blunt leading edge is accounted for. The results suggest that the blunt leading edge can play a key role in explaining the large amplitudes of streaks in that it leads to the deviation from pure isotropy of the FST. The numerical calculation for spanwise localized FST is compared with experimental data of Westin et al. Agreement is obtained except for the amplitude of the disturbances, which is due to the lack of the velocity spectral information of FST in experiment. The viscous secondary instability analysis indicates that there is strong instability in the streaky boundary layer before bypass transition. The maximum growth rate of the unstable modes is larger than that of Tollmien-Schlichting (T-S) waves in the B