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On stability of streamwise streaks and transition thresholds in plane channel flows. (English) Zbl 0927.76029
The authors investigated the linear stability of spanwise periodic streamwise streaks in plane Couette and Poiseuille flow for two transition scenarios, namely the streamwise vortex scenario (SV) and the oblique wave scenario (OW). The growth rate of the streak instability increases with vortex amplitude and is of fundamental type. In the second part the authors compared the threshold energies for transitions in the above two scenarios with those for transition initiated by Tollmien-Schlichting waves (TS), two-dimensional optimal disturbances (2DOPT), and random noise. At subcritical Reynolds numbers the threshold energy for transition in plane Poiseuille flow for SV and OW is at least two orders of magnitude lower than that for transition initiated by the TS scenario, and one order of magnitude lower than that for transition initiated by the 2DOPT scenario. At supercritical Reynolds numbers, the TS and 2DOPT scenarios become more competitive.

MSC:
76E05 Parallel shear flows in hydrodynamic stability
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