×

zbMATH — the first resource for mathematics

Transition of streamwise streaks in zero-pressure-gradient boundary layers. (English) Zbl 1163.76359
Summary: A transition scenario initiated by streamwise low- and high-speed streaks in a flat-plate boundary layer is studied. In many shear flows, the perturbations that show the highest potential for transient energy amplification consist of streamwise-aligned vortices. Due to the lift-up mechanism these optimal disturbances lead to elongated streamwise streaks downstream, with significant spanwise modulation. In a previous investigation P. Andersson, L. Brandt, A. Bottaro and D. S. Henningson [J. Fluid Mech. 428, 29–60 (2001; Zbl 0983.76025)] , the stability of these streaks in a zero-pressure-gradient boundary layer was studied by means of Floquet theory and numerical simulations. The sinuous instability mode was found to be the most dangerous disturbance. We present here the first simulation of the breakdown to turbulence originating from the sinuous instability of streamwise streaks. The main structures observed during the transition process consist of elongated quasi-streamwise vortices located on the flanks of the low-speed streak. Vortices of alternating sign are overlapping in the streamwise direction in a staggered pattern. The present scenario is compared with transition initiated by Tollmien-Schlichting waves and their secondary instability and by-pass transition initiated by a pair of oblique waves. The relevance of this scenario to transition induced by free-stream turbulence is also discussed.

MSC:
76E05 Parallel shear flows in hydrodynamic stability
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76M22 Spectral methods applied to problems in fluid mechanics
PDF BibTeX XML Cite
Full Text: DOI